1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
2 | \NeedsTeXFormat{LaTeX2e} |
---|
3 | \documentclass[12pt,a4paper]{article} |
---|
4 | |
---|
5 | %-- used packages ------------------------------------------------------ |
---|
6 | |
---|
7 | \usepackage{cite} |
---|
8 | \usepackage{graphicx} |
---|
9 | \usepackage{epsfig} |
---|
10 | \usepackage{amssymb} |
---|
11 | \usepackage{amsmath} |
---|
12 | \usepackage{latexsym} |
---|
13 | |
---|
14 | |
---|
15 | %-- page parameters ------------------------------------------------- |
---|
16 | |
---|
17 | \jot = 1.5ex |
---|
18 | \parskip 5pt plus 1pt |
---|
19 | %\parindent 0pt |
---|
20 | \evensidemargin -0.1in \oddsidemargin -0.1in |
---|
21 | \textwidth 6.5in \textheight 9.4in |
---|
22 | \topmargin -.8cm \headsep 1.0cm |
---|
23 | |
---|
24 | %-- command (re)definitions ----------------------------------------- |
---|
25 | |
---|
26 | \newcommand{\capdef}{} |
---|
27 | %\newcommand{\mycaption}[2][\capdef]{\renewcommand{\capdef}{#2}% |
---|
28 | % \caption[#1]{{\itshape #2}}} |
---|
29 | \newcommand{\mycaption}[2][\capdef]{\renewcommand{\capdef}{#2}% |
---|
30 | \caption[#1]{{\footnotesize #2}}} |
---|
31 | \makeatletter |
---|
32 | \renewcommand{\fnum@table}{\textbf{\tablename~\thetable}} |
---|
33 | \renewcommand{\fnum@figure}{\textbf{\figurename~\thefigure}} |
---|
34 | \makeatother |
---|
35 | \def\ltap{\ \raisebox{-.4ex}{\rlap{$\sim$}} \raisebox{.4ex}{$<$}\ } |
---|
36 | \def\gtap{\ \raisebox{-.4ex}{\rlap{$\sim$}} \raisebox{.4ex}{$>$}\ } |
---|
37 | |
---|
38 | \newcounter{myenumi} |
---|
39 | \newcommand{\myitem}{\refstepcounter{myenumi}\item} |
---|
40 | \renewcommand{\themyenumi}{\roman{myenumi}} |
---|
41 | \newenvironment{mylist}{% |
---|
42 | \setcounter{myenumi}{0} |
---|
43 | \begin{list}{\textit{\themyenumi)}}{% |
---|
44 | \setlength{\topsep}{0.2\baselineskip}% |
---|
45 | \setlength{\partopsep}{-\topsep}% |
---|
46 | \setlength{\itemsep}{\topsep}% |
---|
47 | \setlength{\parsep}{0\baselineskip}% |
---|
48 | \setlength{\leftmargin}{0em}% |
---|
49 | \setlength{\listparindent}{\parindent}% |
---|
50 | \setlength{\itemindent}{2.5em}% |
---|
51 | \setlength{\labelwidth}{1.5em}% |
---|
52 | \setlength{\labelsep}{0.75em}}}% |
---|
53 | {\end{list}} |
---|
54 | |
---|
55 | \newlength{\myem} |
---|
56 | \settowidth{\myem}{m} |
---|
57 | \newcommand{\sep}[1]{#1} |
---|
58 | \newcounter{mysubequation}[equation] |
---|
59 | \renewcommand{\themysubequation}{\alph{mysubequation}} |
---|
60 | \newcommand{\mytag}{\stepcounter{mysubequation}% |
---|
61 | \tag{\theequation\protect\sep{\themysubequation}}} |
---|
62 | \newcommand{\globallabel}[1]{\refstepcounter{equation}\label{#1}} |
---|
63 | |
---|
64 | \makeatletter |
---|
65 | \renewcommand{\section}{\@startsection{section}{1}{0em}{-\baselineskip}% |
---|
66 | {\baselineskip}{\normalfont\large\bfseries}} |
---|
67 | \renewcommand{\subsection}% |
---|
68 | {\@startsection{subsection}{2}{0em}{-0.7\baselineskip}% |
---|
69 | {0.7\baselineskip}{\normalfont\bfseries}} |
---|
70 | \makeatother |
---|
71 | |
---|
72 | |
---|
73 | %%%%%%%%%%%%%%%%%%%%%%%% |
---|
74 | % definitions |
---|
75 | %%%%%%%%%%%%%%%%%%%%%%%% |
---|
76 | \newcommand{\centre}[2]{\multispan{#1}{\hfill #2\hfill}} |
---|
77 | \newcommand{\etal}{\textit{et al.}} |
---|
78 | \newcommand{\stheta}{\ensuremath{\sin^22\theta_{13}}} |
---|
79 | \newcommand{\BB}{$\beta$B} |
---|
80 | \newcommand{\sigdm}{\ensuremath{{\rm sign}(\Delta m^2_{31})}} |
---|
81 | \newcommand{\delCP}{\ensuremath{\delta_{\rm CP}}} |
---|
82 | \newcommand{\thetatt}{\ensuremath{\theta_{23}}} |
---|
83 | |
---|
84 | \def\nubar{$\overline{\nu}\ $} |
---|
85 | \def\nue{\ensuremath{\nu_{e}}} |
---|
86 | \def\nubare{\ensuremath{\overline{\nu}_{e}}} |
---|
87 | \def\nubarecc{$\overline{\nu}_{e}^{CC}\ $} |
---|
88 | \def\numu{\ensuremath{\nu_{\mu}\ }} |
---|
89 | \def\nubarmu{\ensuremath{\overline{\nu}_{\mu}}} |
---|
90 | \def\nubarmucc{$\overline{\nu}_{\mu}^{CC}\ $} |
---|
91 | \def\nutau{\ensuremath{\nu_{\tau}\ }} |
---|
92 | \def\nubartau{\ensuremath{\overline{\nu}_{\tau}}} |
---|
93 | \newcommand{\nuenumu}{\ensuremath{\nue \rightarrow \numu\,}} |
---|
94 | \newcommand{\numunutau}{\ensuremath{\numu \rightarrow \nutau\,}} |
---|
95 | \newcommand{\nuenutau}{\ensuremath{\nue \rightarrow \nutau}} |
---|
96 | \newcommand{\nubarenubarmu}{\ensuremath{\overline{\nu}_e \rightarrow \overline{\nu}_\mu\,}} |
---|
97 | \newcommand{\nubarmunubare}{\ensuremath{\overline{\nu}_\mu \rightarrow \overline{\nu}_e\,}} |
---|
98 | \newcommand{\dmot}{\ensuremath{\Delta m^2_{12}\,}} |
---|
99 | |
---|
100 | \newcommand{\He}{\ensuremath{^6{\mathrm{He}}}} |
---|
101 | \newcommand{\Ne}{\ensuremath{^{18}{\mathrm{Ne}}}} |
---|
102 | \def\Li{^6{\mathrm{Li}}} |
---|
103 | \def\anue{\overline{{\mathrm\nu}}_{\mathrm e}} |
---|
104 | \def\anumu{\overline{{\mathrm\nu}}_{\mathrm \mu}} |
---|
105 | \newcommand{\thetaot}{\ensuremath{\theta_{13}}\,} |
---|
106 | \newcommand{\numunue}{\ensuremath{\nu_\mu \rightarrow \nu_e}} |
---|
107 | \newcommand{\nueovernumu}{\ensuremath{\nue/\numu}} |
---|
108 | |
---|
109 | \newcommand{\Efin}{E^\text{fin}} |
---|
110 | \newcommand{\Emin}{E_\text{min}} |
---|
111 | |
---|
112 | |
---|
113 | \begin{document} |
---|
114 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
115 | %%%% Title-page %%%% |
---|
116 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
117 | |
---|
118 | %\begin{titlepage} |
---|
119 | |
---|
120 | % the footnote symbols are only redefined for the title page ! |
---|
121 | \renewcommand{\thefootnote}{\alph{footnote}} |
---|
122 | |
---|
123 | \begin{flushright} |
---|
124 | LAL-06-35\\ |
---|
125 | IC/2006/011\\ |
---|
126 | SISSA 16/2006/EP\\ |
---|
127 | \end{flushright} |
---|
128 | |
---|
129 | \vspace*{0.5cm} |
---|
130 | |
---|
131 | \renewcommand{\thefootnote}{\fnsymbol{footnote}} |
---|
132 | \setcounter{footnote}{-1} |
---|
133 | |
---|
134 | {\begin{center} |
---|
135 | {\Large\textbf{ |
---|
136 | Physics potential of the CERN--MEMPHYS\\[2mm] |
---|
137 | neutrino oscillation project} |
---|
138 | } |
---|
139 | \end{center}} |
---|
140 | |
---|
141 | \vspace*{0.5cm} |
---|
142 | |
---|
143 | \begin{center} {\bf |
---|
144 | J.-E.\ Campagne$^a$, |
---|
145 | M.\ Maltoni$^b$, |
---|
146 | M.\ Mezzetto$^c$, and |
---|
147 | T.\ Schwetz$^d$} |
---|
148 | \end{center} |
---|
149 | |
---|
150 | {\it |
---|
151 | \begin{center} |
---|
152 | $^a$Laboratoire de l'Acc\'el\'erateur Lin\'eaire, |
---|
153 | Universit\'e Paris-Sud, IN2P3/CNRS\\ |
---|
154 | B.P.\ 34, 91898 Orsay Cedex, France\\[2mm] |
---|
155 | % |
---|
156 | $^b$International Centre for Theoretical Physics, |
---|
157 | Strada Costiera 11, I-31014 Trieste, Italy\\ |
---|
158 | {\rm and}\\ |
---|
159 | Departamento de F\'isica Te\'orica \& Instituto de F\'isica Te\'orica, |
---|
160 | Facultad de Ciencias C-XI,\\ |
---|
161 | Universidad Aut\'onoma de Madrid, Cantoblanco, E-28049 Madrid, Spain\\[2mm] |
---|
162 | % |
---|
163 | $^c$Istituto Nazionale Fisica Nucleare, Sezione di Padova, |
---|
164 | Via Marzolo 8, 35100 Padova, Italy\\[2mm] |
---|
165 | % |
---|
166 | $^d$Scuola Internazionale Superiore di Studi Avanzati, |
---|
167 | Via Beirut 2--4, 34014 Trieste, Italy\\ |
---|
168 | {\rm and}\\ |
---|
169 | CERN, Physics Department, Theory Division, CH-1211 Geneva 23, Switzerland |
---|
170 | \end{center}} |
---|
171 | |
---|
172 | \vspace*{0.5cm} |
---|
173 | |
---|
174 | |
---|
175 | \begin{abstract} |
---|
176 | We consider the physics potential of CERN based neutrino oscillation |
---|
177 | experiments consisting of a Beta Beam (\BB) and a Super Beam (SPL) |
---|
178 | sending neutrinos to MEMPHYS, a 440~kt water \v{C}erenkov detector at |
---|
179 | Fr\'ejus, at a distance of 130~km from CERN. The $\theta_{13}$ |
---|
180 | discovery reach and the sensitivity to CP violation are investigated, |
---|
181 | including a detailed discussion of parameter degeneracies and |
---|
182 | systematical errors. For SPL sensitivities similar to the ones of the |
---|
183 | phase~II of the T2K experiment (T2HK) are obtained, whereas the \BB\ |
---|
184 | may reach significantly better sensitivities, depending on the |
---|
185 | achieved number of total ion decays. The results for the |
---|
186 | CERN--MEMPHYS experiments are less affected by systematical |
---|
187 | uncertainties than T2HK. |
---|
188 | % |
---|
189 | We point out that by a combination of data from \BB\ and SPL a |
---|
190 | measurement with antineutrinos is not necessary and hence the same |
---|
191 | physics results can be obtained within about half of the measurement time |
---|
192 | compared to one single experiment. |
---|
193 | % |
---|
194 | Furthermore, it is shown how including data from atmospheric neutrinos in |
---|
195 | the MEMPHYS detector allows to resolve parameter degeneracies and, in |
---|
196 | particular, provides sensitivity to the neutrino mass hierarchy and |
---|
197 | the octant of $\theta_{23}$. |
---|
198 | %\pacs{14.60.Pq, 14.60.Lm} |
---|
199 | \end{abstract} |
---|
200 | |
---|
201 | \renewcommand{\thefootnote}{\arabic{footnote}} |
---|
202 | \setcounter{footnote}{0} |
---|
203 | |
---|
204 | \newpage |
---|
205 | %\tableofcontents |
---|
206 | |
---|
207 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
208 | \section{Introduction} |
---|
209 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
210 | |
---|
211 | In recent years strong evidence for neutrino oscillations has been |
---|
212 | obtained in solar~\cite{solar}, |
---|
213 | atmospheric~\cite{Fukuda:1998mi,Ashie:2005ik}, |
---|
214 | reactor~\cite{Araki:2004mb}, and accelerator~\cite{Aliu:2004sq} |
---|
215 | neutrino experiments. The very near future of long-baseline (LBL) |
---|
216 | neutrino experiments is devoted to the study of the oscillation |
---|
217 | mechanism in the range of $\Delta m^2_{31} \approx 2.4\times10^{-3} \: |
---|
218 | \mathrm{eV}^2$ indicated by atmospheric neutrinos using conventional |
---|
219 | $\nu_\mu$ beams. Similar as in the K2K experiment in |
---|
220 | Japan~\cite{Aliu:2004sq}, the presently running MINOS experiment in |
---|
221 | the USA~\cite{MINOS} uses a low energy beam to measure $\Delta |
---|
222 | m^2_{31}$ by observing the $\nu_\mu\rightarrow\nu_\mu$ disappearance |
---|
223 | probability, while the OPERA~\cite{OPERA} experiment will be able to |
---|
224 | detect $\nu_\tau$ appearance within the high energy CERN--Gran Sasso |
---|
225 | beam~\cite{CNGS}. |
---|
226 | % |
---|
227 | If we do not consider the LSND anomaly~\cite{LSND} that will be |
---|
228 | further studied soon by the MiniBooNE experiment~\cite{MINIBOONE}, all |
---|
229 | data can be accommodated within the three flavor scenario (see |
---|
230 | Refs.~\cite{FOGLILISI05,Maltoni:2004ei} for recent global analyses), |
---|
231 | and neutrino oscillations are described by two neutrino mass-squared |
---|
232 | differences ($\Delta m^2_{21}$ and $\Delta m^2_{31}$) and the $3\times |
---|
233 | 3$ unitary Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton mixing |
---|
234 | matrix~\cite{PMNS} with three angles |
---|
235 | ($\theta_{12}$,$\theta_{13}$,$\theta_{23}$) and one Dirac CP phase |
---|
236 | $\delCP$. |
---|
237 | |
---|
238 | Future tasks of neutrino physics are an improved sensitivity to the |
---|
239 | last unknown mixing angle, $\theta_{13}$, to explore the CP violation |
---|
240 | mechanism in the leptonic sector, and to determine the sign of $\Delta |
---|
241 | m^2_{31}$ which describes the type of the neutrino mass hierarchy |
---|
242 | (normal, $\Delta m^2_{31} > 0$ or inverted, $\Delta m^2_{31} < 0$). |
---|
243 | % |
---|
244 | The present upper bound on $\theta_{13}$ is dominated by the |
---|
245 | constraint from the Chooz reactor experiment~\cite{CHOOZ}. A global |
---|
246 | analysis of all data yields $\sin^22\theta_{13}<0.082$ at |
---|
247 | 90\%~CL~\cite{Maltoni:2004ei}. A main purpose of upcoming reactor and |
---|
248 | accelerator experiments is to improve this bound or to reveal a finite |
---|
249 | value of $\theta_{13}$. In reactor experiments, one uses $\bar{\nu}_e$ |
---|
250 | in disappearance mode and the sensitivity is increased with respect to |
---|
251 | present experiments by the use of a near detector close to the |
---|
252 | reactor~\cite{Wpaper}. In accelerator experiments, the first |
---|
253 | generation of so-called Super Beams with sub-mega watt proton drivers |
---|
254 | such as T2K (phase-I)~\cite{T2K} and NO$\nu$A~\cite{Ayres:2004js}, the |
---|
255 | appearance channel $\nu_\mu\to\nu_e$ is explored. This next generation |
---|
256 | of reactor and Super Beam experiments will reach sensitivities of the |
---|
257 | order of $\sin^22\theta_{13} \lesssim 0.01$ ($90\%$~CL) within a time |
---|
258 | scale of several years~\cite{Huber:2003pm}. |
---|
259 | % |
---|
260 | Beyond this medium term program, there are several projects on how to |
---|
261 | enter the high precision age in neutrino oscillations and to attack |
---|
262 | the ultimate goals like the discovery of leptonic CP violation or the |
---|
263 | determination of the neutrino mass hierarchy. In accelerator |
---|
264 | experiments, one can extend the Super Beam concept by moving to |
---|
265 | multi-mega watt proton drivers~\cite{T2K,Albrow:2005kw,SPL,BNLHS} or |
---|
266 | apply novel technologies, such as neutrino beams from decaying ions |
---|
267 | (so-called Beta Beams)~\cite{zucchelli,Albright:2004iw} or from |
---|
268 | decaying muons (so-called Neutrino |
---|
269 | Factories)~\cite{Albright:2004iw,Blondel:2004ae}. |
---|
270 | |
---|
271 | In this work we focus on possible future neutrino oscillation |
---|
272 | facilities hosted at CERN, namely a multi-mega watt Super Beam |
---|
273 | experiment based on a Super Proton Linac (SPL)~\cite{Campagne:2004wt} |
---|
274 | and a $\gamma = 100$ Beta Beam |
---|
275 | (\BB)~\cite{Mezzetto:2003ub}. These experiments will search for |
---|
276 | $\stackrel{\scriptscriptstyle (-)}{\nu}_\mu \to |
---|
277 | \stackrel{\scriptscriptstyle(-)}{\nu}_e$ and |
---|
278 | $\stackrel{\scriptscriptstyle (-)}{\nu}_e \to |
---|
279 | \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$ appearance, respectively, |
---|
280 | by sending the neutrinos to a mega ton scale water \v{C}erenkov |
---|
281 | detector (MEMPHYS)~\cite{memphys}, located at a distance of 130~km from |
---|
282 | CERN under the Fr\'ejus mountain. Similar detectors are under |
---|
283 | consideration also in the US (UNO~\cite{UNO}) and in Japan |
---|
284 | (Hyper-K~\cite{T2K,Nakamura:2003hk}). |
---|
285 | % |
---|
286 | We perform a detailed analysis of the SPL and \BB\ physics |
---|
287 | potential, discussing the discovery reach for $\theta_{13}$ and |
---|
288 | leptonic CP violation. In addition we consider the possibility to |
---|
289 | resolve parameter degeneracies in the LBL data by using the |
---|
290 | atmospheric neutrinos available in the mega ton |
---|
291 | detector~\cite{Huber:2005ep}. This leads to a sensitivity to the |
---|
292 | neutrino mass hierarchy of the CERN--MEMPHYS experiments, despite the |
---|
293 | rather short baseline. |
---|
294 | % |
---|
295 | The physics performances of \BB\ and SPL are compared to the ones |
---|
296 | obtainable at the second phase of the T2K experiment in Japan, which |
---|
297 | is based on an upgraded version of the original T2K beam and the |
---|
298 | Hyper-K detector (T2HK)~\cite{T2K}. |
---|
299 | |
---|
300 | The outline of the paper is as follows. In Sec.~\ref{sec:analysis} we |
---|
301 | summarize the main characteristics of the \BB, SPL, and T2HK |
---|
302 | experiments and give general details of the physics analysis methods, |
---|
303 | whereas in Sec.~\ref{sec:experiments} we describe in some detail the |
---|
304 | MEMPHYS detector, the \BB, the SPL Super Beam, and our atmospheric |
---|
305 | neutrino analysis. In Sec.~\ref{sec:degeneracies} we review the |
---|
306 | problem of parameter degeneracies and discuss its implications for the |
---|
307 | experiments under consideration. In Sec.~\ref{sec:sensitivities} we |
---|
308 | present the sensitivities to the ``atmospheric parameters'' |
---|
309 | $\theta_{23}$ and $\Delta m^2_{31}$, the $\theta_{13}$ discovery |
---|
310 | potential, and the sensitivity to CP violation. We also investigate in |
---|
311 | some detail the impact of systematical errors. In |
---|
312 | Sec.~\ref{sec:synergies} we discuss synergies which are offered by the |
---|
313 | CERN--MEMPHYS facilities. We point out advantages of the case when |
---|
314 | \BB\ and SPL are available simultaneously, and we consider the use of |
---|
315 | atmospheric neutrino data in MEMPHYS in combination with the LBL |
---|
316 | experiments. Our results are summarized in Sec.~\ref{sec:conclusions}. |
---|
317 | |
---|
318 | |
---|
319 | |
---|
320 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
321 | \section{Experiments overview and analysis methods} |
---|
322 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
323 | \label{sec:analysis} |
---|
324 | |
---|
325 | In this section we give the most important experimental parameters |
---|
326 | which we adopt for the simulation of the CERN--MEMPHYS experiments |
---|
327 | \BB\ and SPL, as well as for the T2HK experiment in Japan. These |
---|
328 | parameters are summarized in Tab.~\ref{tab:setups}. For all |
---|
329 | experiments the detector mass is 440~kt, and the running time is 10 |
---|
330 | years, with a division in neutrino and antineutrino running time in |
---|
331 | such a way that roughly an equal number of events is obtained. We |
---|
332 | always use the total available information from appearance as well as |
---|
333 | disappearance channels including the energy spectrum. For all three |
---|
334 | experiments we adopt rather optimistic values for the systematical |
---|
335 | uncertainties of 2\% as default values, but we also consider the case |
---|
336 | when systematics are increased to 5\%. These errors are uncorrelated |
---|
337 | between the various signal channels (neutrinos and antineutrinos), and |
---|
338 | between signals and backgrounds. |
---|
339 | |
---|
340 | \begin{table} |
---|
341 | \centering |
---|
342 | \begin{tabular}{lcc@{\qquad\qquad}c} |
---|
343 | \hline\noalign{\smallskip} |
---|
344 | & \BB & SPL & T2HK \\ |
---|
345 | \noalign{\smallskip}\hline\noalign{\smallskip} |
---|
346 | Detector mass & 440~kt & 440~kt & 440~kt\\ |
---|
347 | Baseline & 130 km & 130 km & 295 km \\ |
---|
348 | Running time ($\nu + \bar\nu$) |
---|
349 | & 5 + 5 yr & 2 + 8 yr & 2 + 8 yr \\ |
---|
350 | Beam intensity & $5.8\,(2.2) \cdot 10^{18}$ He (Ne) dcys/yr & 4 MW & 4 MW\\ |
---|
351 | Systematics on signal & 2\% & 2\% & 2\%\\ |
---|
352 | Systematics on backgr. & 2\% & 2\% & 2\%\\ |
---|
353 | \noalign{\smallskip}\hline |
---|
354 | \end{tabular} |
---|
355 | \mycaption{Summary of default parameters used for the simulation of the |
---|
356 | \BB, SPL, and T2HK experiments.\label{tab:setups}} |
---|
357 | \end{table} |
---|
358 | |
---|
359 | A more detailed description of the CERN--MEMPHYS experiments is given |
---|
360 | in Sec.~\ref{sec:experiments}. For the T2HK simulation we use the |
---|
361 | setup provided by GLoBES~\cite{Globes} based on |
---|
362 | Ref.~\cite{Huber:2002mx}, which follows closely the LOI~\cite{T2K}. In |
---|
363 | order to allow a fair comparison we introduce the following changes |
---|
364 | with respect to the configuration used in Ref.~\cite{Huber:2002mx}: |
---|
365 | The fiducial mass is set to 440~kt, the systematical errors on the |
---|
366 | background and on the $\nu_e$ and $\bar\nu_e$ appearance signals is |
---|
367 | set to 2\%, and we use a total running time of 10 years, divided into |
---|
368 | 2 years of data taking with neutrinos and 8 years with |
---|
369 | antineutrinos. We include an additional background from the |
---|
370 | $\bar\nu_\mu \to \bar\nu_e$ ($\nu_\mu \to \nu_e$) channel in the |
---|
371 | neutrino (antineutrino) mode. Furthermore, we use |
---|
372 | the same CC detection cross section as for the \BB/SPL |
---|
373 | analysis~\cite{Nuance}. For more details see |
---|
374 | Refs.~\cite{T2K,Huber:2002mx}. |
---|
375 | |
---|
376 | Recently the idea was put forward to observe the T2K beam with a |
---|
377 | second detector placed in |
---|
378 | Korea~\cite{Ishitsuka:2005qi,Kajita:2006bt,Hagiwara:2005pe}. In the |
---|
379 | so-called T2KK setup the Hyper-Kamiokande detector is split into two |
---|
380 | detectors of 270~kt each, one of them is located in Korea at a |
---|
381 | distance of about 1050~km from the source, and the other is placed at |
---|
382 | Kamioka at a distance of 295~km. Here we will confine ourselves to the |
---|
383 | standard T2HK setup, since the purpose of our work is not a T2HK |
---|
384 | optimization study investigating various configurations for that |
---|
385 | experiment. In contrast, here T2HK mainly serves as a point of |
---|
386 | reference to which we compare the CERN--MEMPHYS experiments. For this |
---|
387 | aim we prefer to stick to the ``minimal'' one-detector configuration |
---|
388 | at a relatively short baseline, since two-detector setups with very |
---|
389 | long baselines clearly represent a different class of experiments |
---|
390 | whose consideration goes beyond the scope of the present |
---|
391 | work. Nevertheless we will comment briefly also on T2KK performances |
---|
392 | obtained in Refs.~\cite{Ishitsuka:2005qi,Kajita:2006bt}. |
---|
393 | |
---|
394 | |
---|
395 | \begin{table} |
---|
396 | \centering |
---|
397 | \begin{tabular}{lcccccc} |
---|
398 | \hline\noalign{\smallskip} |
---|
399 | & \centre{2}{\BB} & \centre{2}{SPL} & \centre{2}{T2HK} \\ |
---|
400 | \noalign{\smallskip}\hline\noalign{\smallskip} |
---|
401 | & $\delCP=0$ & $\delCP=\pi/2$ & $\delCP=0$ & $\delCP=\pi/2$ & $\delCP=0$ & $\delCP=\pi/2$\\ |
---|
402 | \noalign{\smallskip}\hline\noalign{\smallskip} |
---|
403 | % |
---|
404 | appearance $\nu$ & & & & & & \\ |
---|
405 | background & \centre{2}{143} &\centre{2}{622} &\centre{2}{898}\\ |
---|
406 | $\stheta=0$ & \centre{2}{28} &\centre{2}{51} &\centre{2}{83} \\ |
---|
407 | $\stheta=10^{-3}$& 76 & 88 & 105 & 14 & 178 & 17 \\ |
---|
408 | $\stheta=10^{-2}$& 326 & 365 & 423 & 137 & 746 & 238 \\ |
---|
409 | % |
---|
410 | \noalign{\smallskip}\hline\noalign{\smallskip} |
---|
411 | % |
---|
412 | appearance $\bar\nu$ & & & & & & \\ |
---|
413 | background & \centre{2}{157} &\centre{2}{640} &\centre{2}{1510}\\ |
---|
414 | $\stheta=0$ & \centre{2}{31} &\centre{2}{57} &\centre{2}{93} \\ |
---|
415 | $\stheta=10^{-3}$& 83 & 12 & 102 & 146 & 192 & 269 \\ |
---|
416 | $\stheta=10^{-2}$& 351 & 126 & 376 & 516 & 762 & 1007 \\ |
---|
417 | % |
---|
418 | \noalign{\smallskip}\hline\noalign{\smallskip} |
---|
419 | % |
---|
420 | disapp. $\nu$ &\centre{2}{100315}&\centre{2}{21653}&\centre{2}{24949}\\ |
---|
421 | background & \centre{2}{6} &\centre{2}{1} &\centre{2}{444}\\ |
---|
422 | disapp. $\bar\nu$&\centre{2}{84125}&\centre{2}{18321}&\centre{2}{34650}\\ |
---|
423 | background &\centre{2}{5} &\centre{2}{1} &\centre{2}{725}\\ |
---|
424 | \noalign{\smallskip}\hline |
---|
425 | % |
---|
426 | \end{tabular} |
---|
427 | \mycaption{Number of events for appearance and disappearance signals |
---|
428 | and backgrounds for the \BB, SPL, and T2HK experiments as |
---|
429 | defined in Tab.~\ref{tab:setups}. For the appearance signals the |
---|
430 | event numbers are given for several values of $\stheta$ and $\delCP |
---|
431 | = 0$ and $\pi/2$. The background as well as the disappearance event |
---|
432 | numbers correspond to $\theta_{13}=0$. For the other oscillation |
---|
433 | parameters the values of Eq.~(\ref{eq:default-params}) are |
---|
434 | used.\label{tab:events}} |
---|
435 | \end{table} |
---|
436 | |
---|
437 | In Tab.~\ref{tab:events} we give the number of signal and background |
---|
438 | events for the experiment setups as defined in Tab.~\ref{tab:setups}. |
---|
439 | For the appearance channels ($\stackrel{\scriptscriptstyle (-)}{\nu}_e |
---|
440 | \to \stackrel{\scriptscriptstyle(-)}{\nu}_\mu$ for the \BB\ and |
---|
441 | $\stackrel{\scriptscriptstyle (-)}{\nu}_\mu \to |
---|
442 | \stackrel{\scriptscriptstyle(-)}{\nu}_e$ for SPL and T2HK) we give the |
---|
443 | signal events for various values of $\theta_{13}$ and $\delCP$. The |
---|
444 | ``signal'' events for $\theta_{13} = 0$ are appearance events induced by |
---|
445 | the oscillations with $\Delta m^2_{21}$. The value $\stheta = 10^{-3}$ |
---|
446 | corresponds roughly to the sensitivity limit for the considered |
---|
447 | experiments, whereas $\stheta = 10^{-2}$ gives a good sensitivity |
---|
448 | to CP violation. This can be appreciated by comparing the values of |
---|
449 | $\nu$ and $\bar\nu$ appearance events for $\delCP = 0$ and $\pi/2$. In |
---|
450 | the table the background to the appearance signal is given for |
---|
451 | $\theta_{13} = 0$. Note that in general the number of background |
---|
452 | events depends also on the oscillation parameters, since also the |
---|
453 | background neutrinos in the beam oscillate. This effect is |
---|
454 | consistently taken into account in the analysis, however, for the |
---|
455 | parameter values in the table the change in the background events due |
---|
456 | to oscillations is only of the order of a few events. |
---|
457 | |
---|
458 | The physics analysis is performed with the GLoBES open source |
---|
459 | software~\cite{Globes}, which provides a convenient tool to simulate |
---|
460 | long-baseline experiments and compare different facilities in a |
---|
461 | unified framework. The experiment definition (AEDL) files for the \BB\ |
---|
462 | and SPL simulation with GLoBES are available at Ref.~\cite{Globes}. |
---|
463 | In the analysis parameter degeneracies and correlations are fully |
---|
464 | taken into account and in general all oscillation parameters are |
---|
465 | varied in the fit. |
---|
466 | % |
---|
467 | To simulate the ``data'' we adopt the following |
---|
468 | set of ``true values'' for the oscillation parameters: |
---|
469 | % |
---|
470 | \begin{equation}\label{eq:default-params} |
---|
471 | \begin{array}{l@{\qquad}l} |
---|
472 | \Delta m^2_{31} = +2.4 \times 10^{-3}~\mathrm{eV}^2\,, & |
---|
473 | \sin^2\theta_{23} = 0.5\,,\\ |
---|
474 | \Delta m^2_{21} = 7.9 \times 10^{-5}~\mathrm{eV}^2 \,,& |
---|
475 | \sin^2\theta_{12} = 0.3 \,, |
---|
476 | \end{array} |
---|
477 | \end{equation} |
---|
478 | % |
---|
479 | and we include a prior knowledge of these values with an accuracy of |
---|
480 | 10\% for $\theta_{12}$, $\theta_{23}$, $\Delta m^2_{31}$, and 4\% for |
---|
481 | $\Delta m^2_{21}$ at 1$\sigma$. These values and accuracies are |
---|
482 | motivated by recent global fits to neutrino oscillation |
---|
483 | data~\cite{FOGLILISI05,Maltoni:2004ei}, and they are always used |
---|
484 | except where explicitly stated otherwise. |
---|
485 | |
---|
486 | |
---|
487 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
488 | \section{The CERN--MEMPHYS experiments} |
---|
489 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
490 | \label{sec:experiments} |
---|
491 | |
---|
492 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
493 | \subsection{The MEMPHYS detector} |
---|
494 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
495 | |
---|
496 | MEMPHYS (MEgaton Mass PHYSics)~\cite{memphys} is a mega ton class |
---|
497 | water \v{C}erenkov detector in the straight extrapolation of |
---|
498 | Super-Kamiokande, located at Fr\'ejus, at a distance of 130~km from |
---|
499 | CERN. It is an alternative design of the UNO~\cite{UNO} and |
---|
500 | Hyper-Kamiokande~\cite{Nakamura:2003hk} detectors and shares the same |
---|
501 | physics case, both from the non-accelerator domain (nucleon decay, |
---|
502 | super nova neutrino detection, solar neutrinos, atmospheric neutrinos) |
---|
503 | and from the accelerator domain which is the subject of this paper. A |
---|
504 | recent civil engineering pre-study to envisage the possibly of large |
---|
505 | cavity excavation located under the Fr\'ejus mountain (4800~m.e.w.) |
---|
506 | near the present Modane underground laboratory has been undertaken. |
---|
507 | The main result of this pre-study is that MEMPHYS may be built with |
---|
508 | present techniques as a modular detector consisting of several shafts, |
---|
509 | each with 65~m in diameter, 65~m in height for the total water |
---|
510 | containment. A schematic view of the layout is shown in |
---|
511 | Fig.~\ref{fig:MEMPHYS}. For the present study we have chosen a |
---|
512 | fiducial mass of 440~kt which means 3 shafts and an inner detector of |
---|
513 | 57~m in diameter and 57~m in height. Each inner detector may be |
---|
514 | equipped with photo detectors (81000 per shaft) with a 30\% |
---|
515 | geometrical coverage and the same photo-statistics as Super-Kamiokande |
---|
516 | (with a 40\% coverage). In principle up to 5 shafts are possible, |
---|
517 | corresponding to a fiducial mass of 730~kt. |
---|
518 | % |
---|
519 | The Fr\'ejus site offers a natural protection against cosmic rays by a |
---|
520 | factor $10^6$. If not mentioned otherwise, the event selection and |
---|
521 | particle identification are the Super-Kamiokande algorithms results. |
---|
522 | |
---|
523 | \begin{figure} |
---|
524 | \centering |
---|
525 | \includegraphics[width=0.65\textwidth]{./fig1.eps} |
---|
526 | \mycaption{\label{fig:MEMPHYS}Sketch of the MEMPHYS detector under the |
---|
527 | Fr\'ejus mountain.} |
---|
528 | \end{figure} |
---|
529 | |
---|
530 | |
---|
531 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
532 | \subsection{The $\gamma = 100\times100$ baseline Beta Beam} |
---|
533 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
534 | |
---|
535 | The concept of a Beta Beam (\BB) has been introduced by P.~Zucchelli |
---|
536 | in Ref.~\cite{zucchelli}. Neutrinos are produced by the decay of |
---|
537 | radioactive isotopes which are stored in a decay ring. An important |
---|
538 | parameter is the relativistic gamma factor of the ions, which |
---|
539 | determines the energy of the emitted neutrinos. \BB\ performances have |
---|
540 | been computed previously for $\gamma(\He)= 66$~\cite{Mezzetto:2003ub}, |
---|
541 | 100~\cite{MyNufact04,Donini:2004hu,JJHigh2}, 150~\cite{JJHigh2}, |
---|
542 | 200~\cite{LindnerBB}, 350~\cite{JJHigh2}, |
---|
543 | 500~\cite{JJHigh1,LindnerBB}, 1000~\cite{LindnerBB}, |
---|
544 | 2000~\cite{JJHigh1}, 2488~\cite{Terranova}. Reviews can be found in |
---|
545 | Ref.~\cite{BB-Reviews}, the physics potential of a very low gamma \BB\ |
---|
546 | has been studied in Ref.~\cite{Volpe}. Performances of a \BB\ with |
---|
547 | $\gamma > 150$ are extremely promising, however, they are neither |
---|
548 | based on an existing accelerator complex nor on detailed calculations |
---|
549 | of the ion decay rates. For a CERN based \BB, fluxes have been |
---|
550 | estimated in Ref.~\cite{Lindroos} and a design study is in progress |
---|
551 | for the facility \cite{Eurisol}. In this work we assume an integrated |
---|
552 | flux of neutrinos in 10 years corresponding to $2.9\cdot 10^{19}$ |
---|
553 | useful \He\ decays and $1.1 \cdot 10^{19}$ useful \Ne\ decays. These |
---|
554 | fluxes have been assumed in all the physics papers quoted above, and |
---|
555 | they are two times higher than the baseline fluxes computed in |
---|
556 | Ref.~\cite{Lindroos}. These latter fluxes suffer for the known |
---|
557 | limitations of the PS and SPS synchrotrons at CERN, ways to improve |
---|
558 | them have been delineated in Ref.~\cite{Lindroos-Optimization}. |
---|
559 | |
---|
560 | The infrastructure available at CERN as well as the MEMPHYS |
---|
561 | location at a distance of 130~km suggest a $\gamma$-factor of about |
---|
562 | $100$. Such a value implies a mean neutrino energy of 400~MeV, which |
---|
563 | leads to the oscillation maximum at about 200~km for $\Delta m^2_{31} |
---|
564 | = 2.4\times 10^{-3}$~eV$^2$. We have checked that the performance at |
---|
565 | the somewhat shorter baseline of 130~km is rather similar to the one |
---|
566 | at the oscillation maximum. Moreover, the purpose of this paper is to |
---|
567 | estimate the physics potential for a realistic set-up and not to study |
---|
568 | the optimization of the \BB\ regardless of any logistic consideration |
---|
569 | (see, e.g., Refs.~\cite{LindnerBB,JJHigh2} for such optimization |
---|
570 | studies). |
---|
571 | |
---|
572 | The signal events from the $\nu_e \to \nu_\mu$ neutrino and |
---|
573 | antineutrino appearance channels in the \BB\ are \numu charged current |
---|
574 | (CC) events. The Nuance v3r503 Monte Carlo code~\cite{Nuance} is used |
---|
575 | to generate signal events. The selection for these events is based on |
---|
576 | standard Super-Kamiokande particle identification algorithms. The |
---|
577 | muon identification is reinforced by asking for the detection of the |
---|
578 | Michel decay electron. |
---|
579 | % |
---|
580 | The neutrino energy is reconstructed by smearing momentum and |
---|
581 | direction of the charged lepton with the Super-Kamiokande resolution |
---|
582 | functions, and applying quasi-elastic (QE) kinematics assuming the |
---|
583 | known incoming neutrino direction. Energy reconstruction in the \BB\ |
---|
584 | energy range is remarkably powerful, and the contamination of non-QE |
---|
585 | events very small, as shown in Fig.~\ref{fig:QE-Energy}. |
---|
586 | % |
---|
587 | As pointed out in Ref.~\cite{JJHigh2}, it is necessary to use a |
---|
588 | migration matrix for the neutrino energy reconstruction to properly |
---|
589 | handle Fermi motion smearing and the non-QE event contamination. We |
---|
590 | use 100~MeV bins for the reconstructed energy and 40~MeV bins for the |
---|
591 | true neutrino energy. Four migration matrices (for |
---|
592 | $\nu_e,\bar\nu_e,\nu_\mu,\bar\nu_\mu$) are applied to signal events as |
---|
593 | well as backgrounds. As suggested from Fig.~\ref{fig:QE-Energy} the |
---|
594 | results using migration matrices are very similar to a Gaussian |
---|
595 | energy resolution. |
---|
596 | |
---|
597 | \begin{figure}[!t] |
---|
598 | \centering |
---|
599 | \includegraphics[width=0.65\textwidth]{./fig2.eps} |
---|
600 | \mycaption{\label{fig:QE-Energy} Energy resolution for \nue\ |
---|
601 | interactions in the 200--300~MeV energy range. The quantity |
---|
602 | displayed is the difference between the reconstructed and the true |
---|
603 | neutrino energy.} |
---|
604 | \end{figure} |
---|
605 | |
---|
606 | Backgrounds from charged pions and atmospheric neutrinos are computed |
---|
607 | with the identical analysis chain as signal events. |
---|
608 | Charged pions generated in NC events (or in NC-like events where the |
---|
609 | leading electron goes undetected) are the main source of background for |
---|
610 | the experiment. To compute this background inclusive NC and CC events |
---|
611 | have been generated with the \BB\ spectrum. Events have been selected |
---|
612 | where the only visible track is a charged pion above the \v{C}erenkov |
---|
613 | threshold. Particle identification efficiencies have been applied to |
---|
614 | those particles. The probability for a pion to survive in water until |
---|
615 | its decay has been computed with Geant~3.21 and cross-checked with a |
---|
616 | Fluka~2003 simulation. This probability is different for positive and |
---|
617 | negative pions, the latter having a higher probability to be absorbed |
---|
618 | before decaying. The surviving events are background, and the |
---|
619 | reconstructed neutrino energy is computed misidentifying these pions |
---|
620 | as muons. Event rates are reported in Tab.~\ref{tab:sigbck}. From |
---|
621 | these numbers it becomes evident that requiring the detection of the |
---|
622 | Michel electron provides an efficient cut to eliminate the pion |
---|
623 | background. |
---|
624 | % |
---|
625 | These background rates are significantly smaller than quoted in |
---|
626 | Ref.~\cite{MyNufact04}, where pion decays were computed with the |
---|
627 | same probabilities as for muons and they are slightly different |
---|
628 | from those quoted in Ref.~\cite{ MezzettoNuFact05}, where an |
---|
629 | older version of Nuance had been used. |
---|
630 | % |
---|
631 | The numbers of Tab.~\ref{tab:sigbck} have been cross-checked by |
---|
632 | comparing the Nuance and Neugen~\cite{Neugen} event |
---|
633 | generators, finding a fair agreement in background rates and energy shape. |
---|
634 | |
---|
635 | \begin{table}[t] |
---|
636 | \centering |
---|
637 | \begin{tabular}{l@{\qquad}rrr@{\qquad}rrr} |
---|
638 | \hline\noalign{\smallskip} |
---|
639 | & \multicolumn{3}{ c }{\Ne} & \multicolumn{3}{c}{\He} \\ |
---|
640 | \hline\noalign{\smallskip} |
---|
641 | & \numu CC & $\pi^+$ & $\pi^-$ & \nubarmu CC & $\pi^+$ & $\pi^-$ \\ |
---|
642 | \hline\noalign{\smallskip} |
---|
643 | Generated ev.\ & 115367 & 557 & 341 & 101899 & 674 & 400 \\ |
---|
644 | Particle ID & 95717 & 204 & 100 & 85285 & 240 & 118 \\ |
---|
645 | Decay & 61347 & 107 & 8 & 69242 & 120 & 8 \\ |
---|
646 | \hline\noalign{\smallskip} |
---|
647 | \end{tabular} |
---|
648 | \mycaption{\label{tab:sigbck} Events for the \BB\ in a 4400~kt~yr |
---|
649 | exposure. \numu(\nubarmu) CC events are computed assuming full |
---|
650 | oscillations ($P_{\nu_e\to\nu_\mu} = 1$), and pion backgrounds are |
---|
651 | computed from \nue(\nubare) CC+NC events. In the rows we give the |
---|
652 | number events generated within the fiducial volume (``Generated |
---|
653 | ev.''), after muon particle identification (``Particle ID''), and |
---|
654 | after applying a further identification requiring the detection of |
---|
655 | the Michel electron (``Decay''). } |
---|
656 | \end{table} |
---|
657 | |
---|
658 | Also atmospheric neutrinos can constitute an important source of |
---|
659 | background~\cite{zucchelli,JJHigh2,JJHigh1,MezzettoNuFact05}. This |
---|
660 | background can be suppressed only by keeping a very short duty cycle |
---|
661 | ($2.2 \cdot 10^{-3}$ is the target value for the \BB\ design study), |
---|
662 | and this in turn is one of the most challenging bounds on the design |
---|
663 | of the Beta Beam complex. Following Ref.~\cite{MezzettoNuFact05} we |
---|
664 | include the atmospheric neutrino background based on a Monte Carlo |
---|
665 | simulation using Nuance. Events are reconstructed as if they were |
---|
666 | signal neutrino events. We estimate that 5 events/year would survive |
---|
667 | the analysis chain in a full solar year (the \BB\ should run for about |
---|
668 | 1/3 of this period) and include these events as backgrounds in the |
---|
669 | analysis. Under these circumstances, the present value of the \BB\ |
---|
670 | duty cycle seems to be an overkill, it could be reduced by a factor 5 |
---|
671 | at least, see also Ref.~\cite{MezzettoNuFact05} for a discussion of |
---|
672 | the effect of a higher duty cycle. |
---|
673 | |
---|
674 | |
---|
675 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
676 | \subsection{The $3.5$-GeV SPL Super Beam} |
---|
677 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
678 | |
---|
679 | |
---|
680 | In the recent Conceptual Design Report 2 (CDR2) the foreseen Super |
---|
681 | Proton Linac (SPL)~\cite{SPL} will provide the protons for the muon |
---|
682 | production in the context of a Neutrino Factory, and at a first stage |
---|
683 | will feed protons to a fixed target experiment to produce an intense |
---|
684 | conventional neutrino beam (``Super Beam''). The parameters of the |
---|
685 | beam line take into account the optimization~\cite{Campagne:2004wt} of |
---|
686 | the beam energy as well as the secondary particle focusing and decay |
---|
687 | to search for $\nu_\mu \rightarrow \nu_e$ and $\bar{\nu}_\mu |
---|
688 | \rightarrow \bar{\nu}_e$ appearance as well as $\nu_\mu$, |
---|
689 | $\bar\nu_\mu$ disappearance in a mega ton scale water \v{C}erenkov |
---|
690 | detector. In particular, a full simulation of the beam line from the |
---|
691 | proton on target interaction up to the secondary particle decay tunnel |
---|
692 | has been performed. The proton on a liquid mercury target (30~cm long, |
---|
693 | $7.5$~mm radius, 13.546 density) has been simulated with |
---|
694 | FLUKA~2002.4~\cite{FLUKA} while the horn focusing system and the decay |
---|
695 | tunnel simulation has been preformed with |
---|
696 | GEANT~3.21~\cite{GEANT}.\footnote{Although there are differences |
---|
697 | between the predicted pion and kaon productions as a function of |
---|
698 | proton kinetic energy with FLUKA~2002.4 and 2005.6, the results are |
---|
699 | consistent for the relevant energy of 3.5~GeV. We emphasize that the |
---|
700 | pion and the kaon production cross-sections are waiting for |
---|
701 | experimental confirmation~\cite{HARP-MINERVA} and a new optimization |
---|
702 | would be required if their is a disagreement with the present |
---|
703 | knowledge.} |
---|
704 | |
---|
705 | \begin{figure}[!t] |
---|
706 | \centering |
---|
707 | \includegraphics[width=0.65\textwidth]{./fig3.eps} |
---|
708 | \mycaption{\label{fig:fluxSPLContrib} Neutrino fluxes, at $130$~km |
---|
709 | from the target with the horns focusing the positive particles |
---|
710 | (top panel) or the negative particles (bottom panel). The fluxes are |
---|
711 | computed for a SPL proton beam of $3.5$~GeV (4~MW), a decay tunnel |
---|
712 | with a length of $40$~m and a radius of $2$~m.} |
---|
713 | \end{figure} |
---|
714 | |
---|
715 | Since the optimization requirements for a Neutrino Factory are rather |
---|
716 | different than for a Super Beam the new SPL configuration has a |
---|
717 | significant impact on the physics performance (see |
---|
718 | Ref.~\cite{Campagne:2004wt} for a detailed discussion). The SPL |
---|
719 | fluxes of the four neutrino species ($\nu_\mu$, $\nu_e$, |
---|
720 | $\bar{\nu}_\mu$, $\bar{\nu}_e$) for the positive ($\nu_\mu$ beam) and |
---|
721 | the negative focusing ($\bar{\nu}_\mu$ beam) are show in |
---|
722 | Fig.~\ref{fig:fluxSPLContrib}. The total number of $\nu_\mu$ |
---|
723 | ($\bar{\nu}_\mu$) in positive (negative) focusing is about |
---|
724 | $1.18\,(0.97) \times 10^{12}\:\mathrm{m}^{-2}\mathrm{y}^{-1}$ with an |
---|
725 | average energy of $300$~MeV. The $\nu_e$ ($\bar{\nu}_e$) contamination |
---|
726 | in the $\nu_\mu$ ($\bar\nu_\mu$) beam is around $0.7\%$ |
---|
727 | ($6.0\%$). |
---|
728 | % |
---|
729 | Following Ref.~\cite{Mezzetto:2003mm}, the $\pi^o$ background is |
---|
730 | reduced using a tighter PID cut compared to the standard |
---|
731 | Super-Kamiokande analysis used in K2K, but the cuts are looser than |
---|
732 | for T2K. Indeed, at SPL energies the $\pi^o$ background is less severe |
---|
733 | than for T2HK. This is because the resonant cross section is |
---|
734 | suppressed, and the produced pions have an energy where the angle |
---|
735 | between the two gammas is very wide, leading to a small probability |
---|
736 | that the two gamma rings overlap. This results in a higher signal |
---|
737 | efficiency of SPL compared to T2HK (70\% against 40\%) and a smaller |
---|
738 | rate of $\pi^o$ background. |
---|
739 | % |
---|
740 | The Michel electron is required for the $\mu$ identification. |
---|
741 | % |
---|
742 | For the $\nu_\mu \rightarrow \nu_e$ channel the background consists |
---|
743 | roughly of 90\% $\nu_e \rightarrow \nu_e$ CC interactions, 6\% $\pi^o$ |
---|
744 | from NC interactions, 3\% miss identified muons from $\nu_\mu |
---|
745 | \rightarrow \nu_\mu$ CC, and 1\% $\bar{\nu}_e \rightarrow \bar{\nu}_e$ |
---|
746 | CC interactions. For the $\bar{\nu}_\mu \rightarrow \bar{\nu}_e$ |
---|
747 | channel the contributions to the background are 45\% $\bar{\nu}_e |
---|
748 | \rightarrow \bar{\nu}_e$ CC interactions, 35\% $\nu_e \rightarrow |
---|
749 | \nu_e$ CC interactions, 18\% $\pi^o$ from NC interactions and 2\% miss |
---|
750 | identified muons from $\bar{\nu}_\mu \rightarrow \bar{\nu}_\mu$ CC. |
---|
751 | In addition we include the events from the contamination of |
---|
752 | ``wrong sign'' muon-neutrinos due to $\bar\nu_\mu \to \bar\nu_e$ |
---|
753 | ($\nu_\mu \to \nu_e$) oscillations in the neutrino (antineutrino) |
---|
754 | mode. |
---|
755 | % |
---|
756 | We have checked that with the envisaged duty cycle of $2.4\times |
---|
757 | 10^{-4}$ the background from atmospheric neutrinos is negligible for |
---|
758 | the SPL. |
---|
759 | |
---|
760 | \begin{figure}[!t] |
---|
761 | \centering |
---|
762 | \includegraphics[width=0.5\textwidth]{./fig4.eps} |
---|
763 | % |
---|
764 | \mycaption{\label{fig:fluxComparison} |
---|
765 | Comparison of the fluxes from SPL and \BB.} |
---|
766 | \end{figure} |
---|
767 | |
---|
768 | Considering the signal over square-root of background |
---|
769 | ratio, the $3.5$~GeV beam energy is more favorable than the original |
---|
770 | $2.2$~GeV option. Compared to the fluxes used in |
---|
771 | Refs.~\cite{Mezzetto:2003mm,Donini:2004hu} the gain is at least a |
---|
772 | factor $2.5$ and this justifies to reconsider in detail the physics |
---|
773 | potential of the SPL Super Beam. |
---|
774 | % |
---|
775 | Both the appearance and the disappearance channels are used. For the |
---|
776 | spectral analysis we use 10 bins of 100~MeV in the interval $0 < E_\nu |
---|
777 | < 1$~GeV, applying the same migration matrices as for the \BB\ to take |
---|
778 | into account properly the neutrino energy reconstruction. As ultimate |
---|
779 | goal suggested in Ref.~\cite{T2K} a 2\% systematical error is used as |
---|
780 | default both for signal and background, this would be achieved by a |
---|
781 | special care of the design of the close position. However, we discuss |
---|
782 | also how a 5\% systematical error affects the sensitivities. |
---|
783 | % |
---|
784 | Using neutrino cross-sections on water from Ref.~\cite{Nuance}, the |
---|
785 | number of expected $\nu_\mu$ charged current is about $98$ per |
---|
786 | kt~yr. In Fig.~\ref{fig:fluxComparison} we compare the fluxes from the |
---|
787 | SPL to the one from the \BB. |
---|
788 | |
---|
789 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
790 | \subsection{The atmospheric neutrino analysis} |
---|
791 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
792 | \label{sec:atm-details} |
---|
793 | |
---|
794 | The simulation of atmospheric neutrino data in MEMPHYS is based on the |
---|
795 | analysis presented in Ref.~\cite{Huber:2005ep}, with the following |
---|
796 | differences: |
---|
797 | % |
---|
798 | \begin{itemize} |
---|
799 | \item We replace the neutrino fluxes at Kamioka with those at Gran |
---|
800 | Sasso. We use the Honda calculations~\cite{Honda:2004yz}, which |
---|
801 | unfortunately are not yet available for the Fr\'ejus |
---|
802 | site. However, since the fluxes increase with the geomagnetic |
---|
803 | latitude and Fr\'ejus is northern than Gran Sasso, our choice is |
---|
804 | conservative. |
---|
805 | |
---|
806 | \item We take into account the specific geometry of the MEMPHYS |
---|
807 | detector. This is particularly important to properly separate |
---|
808 | fully contained from partially contained events, as well as |
---|
809 | stopping muon from through-going muon events. |
---|
810 | |
---|
811 | \item We divide our total data sample into 420 different bins: |
---|
812 | fully contained single-ring events, further subdivided according |
---|
813 | to flavor ($e$-like or $\mu$-like), lepton momentum (8 bins: |
---|
814 | 0.1--0.3, 0.3--0.5, 0.5--1, 1--2, 2--3, 3--5, 5--8, |
---|
815 | 8--$\infty$~GeV) and lepton direction (20 bins in zenith angle); |
---|
816 | % |
---|
817 | fully contained multi-ring events, further subdivided according to |
---|
818 | flavor ($e$-like or $\mu$-like), reconstructed neutrino energy (3 |
---|
819 | bins: 0--1.33, 1.33--5, 5--$\infty$~GeV) and lepton direction (10 |
---|
820 | bins in zenith angle); |
---|
821 | % |
---|
822 | partially contained $\mu$-like events, divided into 20 zenith bins; |
---|
823 | % |
---|
824 | up-going muons, divided into stopping and through-going events, and in |
---|
825 | 10 zenith bins each. |
---|
826 | |
---|
827 | \item We include in our calculations the neutral-current |
---|
828 | contamination of each bin. To this extent we assume that the |
---|
829 | ratio between neural-current and \emph{unoscillated} |
---|
830 | charged-current events in MEMPHYS is the same as in |
---|
831 | Super-Kamiokande, and we take this ratio from |
---|
832 | Ref.~\cite{Ashie:2005ik}. |
---|
833 | |
---|
834 | \item We consider also multi-ring events, which we define |
---|
835 | as fully contained charged-current events which are \emph{not} |
---|
836 | tagged as single-ring. Again, we assume that the survival |
---|
837 | efficiency and the NC contamination are the same as for |
---|
838 | Super-Kamiokande~\cite{Ashie:2005ik}. |
---|
839 | \end{itemize} |
---|
840 | |
---|
841 | The expected number of contained events is given by: |
---|
842 | % |
---|
843 | \begin{multline} \label{eq:contained} |
---|
844 | N_b(\vec\omega) = N_b^\text{NC} + |
---|
845 | n_\text{tgt} T \sum_{\alpha,\beta,\pm} |
---|
846 | \int_0^\infty dh \int_{-1}^{+1} dc_\nu |
---|
847 | \int_{\Emin}^\infty dE_\nu \int_{\Emin}^{E_\nu} dE_l |
---|
848 | \int_{-1}^{+1} dc_a \int_0^{2\pi} d\varphi_a |
---|
849 | \\ |
---|
850 | \frac{d^3 \Phi_\alpha^\pm}{dE_\nu \, dc_\nu \, dh}(E_\nu, c_\nu, h) |
---|
851 | \, P_{\alpha\to\beta}^\pm(E_\nu, c_\nu, h \,|\, \vec\omega) |
---|
852 | \, \frac{d^2\sigma_\beta^\pm}{dE_l \, dc_a}(E_\nu, E_l, c_a) |
---|
853 | \, \varepsilon_\beta^b(E_l, c_l(c_\nu, c_a, \varphi_a)) |
---|
854 | \,, |
---|
855 | \end{multline} |
---|
856 | % |
---|
857 | where $P_{\alpha\to\beta}^+$ ($P_{\alpha\to\beta}^-$) is the |
---|
858 | $\nu_\alpha \to \nu_\beta$ ($\bar{\nu}_\alpha \to \bar{\nu}_\beta$) |
---|
859 | conversion probability for given values of the neutrino energy |
---|
860 | $E_\nu$, the cosine $c_\nu$ of the angle between the incoming neutrino |
---|
861 | and the vertical direction, the production altitude $h$, and the |
---|
862 | neutrino oscillation parameters $\vec\omega$. We calculate the |
---|
863 | conversion probability numerically in the general three-flavor |
---|
864 | framework taking into account matter effects from a realistic Earth |
---|
865 | density profile. Further, $N_b^\text{NC}$ is the neutral-current |
---|
866 | background for the bin $b$, $n_\text{tgt}$ is the number of targets, |
---|
867 | $T$ is the experiment running time, $\Phi_\alpha^+$ ($\Phi_\alpha^-$) |
---|
868 | is the flux of atmospheric neutrinos (antineutrinos) of type $\alpha$, |
---|
869 | and $\sigma_\beta^+$ ($\sigma_\beta^-$) is the charged-current |
---|
870 | neutrino- (antineutrino-) nucleon interaction cross section. |
---|
871 | % |
---|
872 | The variable $E_l$ is the energy of the final lepton of type $\beta$, |
---|
873 | while $c_a$ and $\varphi_a$ parametrize the opening angle between the |
---|
874 | incoming neutrino and the final lepton directions as determined by the |
---|
875 | kinematics of the neutrino interaction. |
---|
876 | % |
---|
877 | Finally, $\varepsilon_\beta^b$ gives the probability that a charged |
---|
878 | lepton of type $\beta$, energy $E_l$ and direction $c_l$ contributes |
---|
879 | to the bin $b$. |
---|
880 | |
---|
881 | Up-going muon events are calculated as follows: |
---|
882 | % |
---|
883 | \begin{multline} \label{eq:upgoing} |
---|
884 | N_b(\vec\omega) = \rho_\text{rock} T \sum_{\alpha,\pm} |
---|
885 | \int_0^\infty dh \int_{-1}^{+1} dc_\nu |
---|
886 | \int_{\Emin}^\infty dE_\nu |
---|
887 | \int_{\Emin}^{E_\nu} dE^0_\mu \int_{\Emin}^{E^0_\mu} d\Efin_\mu |
---|
888 | \int_{-1}^{+1} dc_a \int_0^{2\pi} d\varphi_a |
---|
889 | \\ |
---|
890 | \frac{d^3 \Phi_\alpha^\pm}{dE_\nu \, dc_\nu \, dh}(E_\nu, c_\nu, h) |
---|
891 | \, P_{\alpha\to\mu}^\pm(E_\nu, c_\nu, h \,|\, \vec\omega) |
---|
892 | \, \frac{d^2\sigma_\mu^\pm}{dE^0_\mu \, dc_a}(E_\nu, dE^0_\mu, c_a) |
---|
893 | \\ |
---|
894 | \times R_\text{rock}(E^0_\mu,\Efin_\mu) |
---|
895 | \, \mathcal{A}_\text{eff}^b(\Efin_\mu, |
---|
896 | c_l(c_\nu, c_a, \varphi_a)) \,, |
---|
897 | \end{multline} |
---|
898 | % |
---|
899 | where $\rho_\text{rock}$ is the density of targets in standard rock, |
---|
900 | $R_\text{rock}$ is the effective muon range~\cite{Lipari:1991ut} for a |
---|
901 | muon which is produced with energy $E^0_\mu$ and reaches the detector |
---|
902 | with energy $\Efin_\mu$, and $\mathcal{A}_\text{eff}^b$ is the |
---|
903 | effective area for the bin $b$. The other variables and physical |
---|
904 | quantities are the same as for contained events. |
---|
905 | |
---|
906 | The statistical analysis is based on the pull method, as described in |
---|
907 | Ref.~\cite{Gonzalez-Garcia:2004wg}. In our analysis we include three |
---|
908 | different kind of experimental uncertainties: |
---|
909 | % |
---|
910 | Flux uncertainties: total normalization (20\%), tilt factor (5\%), |
---|
911 | zenith angle (5\%), $\nu/\bar\nu$ ratio (5\%), and $\mu/e$ ratio |
---|
912 | (5\%); |
---|
913 | % |
---|
914 | cross-section uncertainties: total normalization (15\%) and $\mu/e$ |
---|
915 | ratio (1\%) for each type of charged-current interaction |
---|
916 | (quasi-elastic, one-pion production, and deep-inelastic scattering), |
---|
917 | and total normalization (15\%) for the neutral-current contributions; |
---|
918 | % |
---|
919 | systematic uncertainties: same as in previous analyses, details are |
---|
920 | given in the Appendix of Ref.~\cite{Gonzalez-Garcia:2004wg}. In |
---|
921 | addition, we assume independent normalization uncertainties (20\%) for |
---|
922 | $e$-like and $\mu$-like multi-ring events. |
---|
923 | % |
---|
924 | Since we are dividing our data sample into a large number of bins, it |
---|
925 | is important to use Poisson statistics as some of the bins contain |
---|
926 | only a few number of events. We therefore write our $\chi^2$ as: |
---|
927 | % |
---|
928 | \begin{equation} \label{eq:poisson} |
---|
929 | \chi^2(\vec\omega) = \min_{\vec\xi} \left[ 2 \sum_b \left( |
---|
930 | N_b^\text{th}(\vec\omega,\, \vec\xi) |
---|
931 | - N_b^\text{ex} + N_b^\text{ex} \ln\frac{N_b^\text{ex}} |
---|
932 | {N_b^\text{th}(\vec\omega,\, \vec\xi)} \right) |
---|
933 | + \sum_n \xi_n^2 \right] \,, |
---|
934 | \end{equation} |
---|
935 | % |
---|
936 | where the number of events for a given value of the pulls $\vec\xi$ is |
---|
937 | given by: |
---|
938 | % |
---|
939 | \begin{equation} \label{eq:theopulls} |
---|
940 | N_b^\text{th}(\vec\omega,\, \vec\xi) = N_b^\text{th}(\vec\omega) \, |
---|
941 | \exp\left( \sum_n \pi_b^n(\vec\omega)\, \xi_n \right) \,. |
---|
942 | \end{equation} |
---|
943 | % |
---|
944 | The use of an exponential dependence on the pulls in |
---|
945 | Eq.~\eqref{eq:theopulls}, rather than the usual linear dependence, |
---|
946 | ensures that the theoretical predictions remain positive for |
---|
947 | \emph{any} value of the pulls, thus avoiding numerical inconsistencies |
---|
948 | during the pull minimization procedure. |
---|
949 | |
---|
950 | |
---|
951 | |
---|
952 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
953 | \section{Degeneracies} |
---|
954 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
955 | \label{sec:degeneracies} |
---|
956 | |
---|
957 | |
---|
958 | A characteristic feature in the analysis of future LBL experiments is |
---|
959 | the presence of {\it parameter degeneracies}. Due to the inherent |
---|
960 | three-flavor structure of the oscillation probabilities, for a given |
---|
961 | experiment in general several disconnected regions in the |
---|
962 | multi-dimensional space of oscillation parameters will be |
---|
963 | present. Traditionally these degeneracies are referred to in the |
---|
964 | following way: |
---|
965 | % |
---|
966 | \begin{itemize} |
---|
967 | \item |
---|
968 | The {\it intrinsic} or |
---|
969 | ($\delCP,\theta_{13}$)-degeneracy~\cite{Burguet-Castell:2001ez}: |
---|
970 | For a measurement based on the $\nu_\mu \to \nu_e$ oscillation probability for |
---|
971 | neutrinos and antineutrinos two disconnected solutions appear in the |
---|
972 | ($\delCP,\theta_{13}$) plane. |
---|
973 | \item |
---|
974 | The {\it hierarchy} or sign($\Delta |
---|
975 | m^2_{31}$)-degeneracy~\cite{Minakata:2001qm}: The two solutions |
---|
976 | corresponding to the two signs of $\Delta m^2_{31}$ appear in general |
---|
977 | at different values of $\delCP$ and $\theta_{13}$. |
---|
978 | \item |
---|
979 | The {\it octant} or $\theta_{23}$-degeneracy~\cite{Fogli:1996pv}: |
---|
980 | Since LBL experiments are sensitive mainly to $\sin^22\theta_{23}$ it |
---|
981 | is difficult to distinguish the two octants $\theta_{23} < \pi/4$ and |
---|
982 | $\theta_{23} > \pi/4$. Again, the solutions corresponding to |
---|
983 | $\theta_{23}$ and $\pi/2 - \theta_{23}$ appear in general at different |
---|
984 | values of $\delCP$ and $\theta_{13}$. |
---|
985 | \end{itemize} |
---|
986 | % |
---|
987 | This leads to an eight-fold ambiguity in $\theta_{13}$ and |
---|
988 | $\delCP$~\cite{Barger:2001yr}, and hence degeneracies provide a |
---|
989 | serious limitation for the determination of $\theta_{13}$, $\delCP$, |
---|
990 | and the sign of $\Delta m^2_{31}$. Recent discussions of degeneracies |
---|
991 | can be found for example in |
---|
992 | Refs.~\cite{Huber:2002mx,Huber:2005ep,Yasuda:2004gu,Ishitsuka:2005qi}; |
---|
993 | degeneracies in the context of CERN--Fr\'ejus \BB\ and SPL have been |
---|
994 | considered previously in Ref.~\cite{Donini:2004hu}. |
---|
995 | % |
---|
996 | In Fig.~\ref{fig:degeneracies} we illustrate the effect of |
---|
997 | degeneracies for the \BB, SPL, and T2HK experiments. Assuming the |
---|
998 | true parameter values $\delta_\mathrm{CP} = -0.85 \pi$, |
---|
999 | $\sin^22\theta_{13} = 0.03$, $\sin^2\theta_{23} = 0.6$ we show the |
---|
1000 | allowed regions in the plane of $\stheta$ and $\delCP$ taking into |
---|
1001 | account the solutions with the wrong hierarchy and the wrong octant of |
---|
1002 | $\theta_{23}$. |
---|
1003 | |
---|
1004 | \begin{figure}[!t] |
---|
1005 | \centering |
---|
1006 | \includegraphics[width=0.95\textwidth]{./fig5.eps} |
---|
1007 | % |
---|
1008 | \mycaption{Allowed regions in $\sin^22\theta_{13}$ and |
---|
1009 | $\delta_\mathrm{CP}$ for LBL data alone (contour lines) and LBL+ATM |
---|
1010 | data combined (colored regions). $\mathrm{H^{tr/wr} (O^{tr/wr})}$ |
---|
1011 | refers to solutions with the true/wrong mass hierarchy (octant of |
---|
1012 | $\theta_{23}$). The true parameter values are $\delta_\mathrm{CP} = |
---|
1013 | -0.85 \pi$, $\sin^22\theta_{13} = 0.03$, $\sin^2\theta_{23} = 0.6$, |
---|
1014 | and the values from Eq.~(\ref{eq:default-params}) for the other |
---|
1015 | parameters. The running time is ($5\nu + 5\bar\nu$)~yrs for \BB\ and |
---|
1016 | ($2\nu + 8\bar\nu$)~yrs for the Super Beams.} |
---|
1017 | \label{fig:degeneracies} |
---|
1018 | \end{figure} |
---|
1019 | |
---|
1020 | |
---|
1021 | \begin{figure}[!t] |
---|
1022 | \centering |
---|
1023 | \includegraphics[width=0.9\textwidth]{./fig6.eps} |
---|
1024 | % |
---|
1025 | \mycaption{Resolving degeneracies in SPL by successively using the |
---|
1026 | appearance rate measurement, disappearance channel rate and |
---|
1027 | spectrum, spectral information in the appearance channel, and |
---|
1028 | atmospheric neutrinos. Allowed regions in $\sin^22\theta_{13}$ and |
---|
1029 | $\delta_\mathrm{CP}$ are shown at 95\%~CL, and $\mathrm{H^{tr/wr} |
---|
1030 | (O^{tr/wr})}$ refers to solutions with the true/wrong mass hierarchy |
---|
1031 | (octant of $\theta_{23}$). The true parameter values are |
---|
1032 | $\delta_\mathrm{CP} = -0.85 \pi$, $\sin^22\theta_{13} = 0.03$, |
---|
1033 | $\sin^2\theta_{23} = 0.6$, and the values from |
---|
1034 | Eq.~(\ref{eq:default-params}) for the other parameters. The running |
---|
1035 | time is ($2\nu + 8\bar\nu$)~yrs. |
---|
1036 | |
---|
1037 | } |
---|
1038 | \label{fig:degeneracies_SPL} |
---|
1039 | \end{figure} |
---|
1040 | |
---|
1041 | As visible in Fig.~\ref{fig:degeneracies} for the |
---|
1042 | Super Beam experiments SPL and T2HK there is only a four-fold |
---|
1043 | degeneracy related to sign($\Delta m^2_{31}$) and the octant of |
---|
1044 | $\theta_{23}$, whereas the intrinsic degeneracy can be resolved. |
---|
1045 | % |
---|
1046 | Several pieces of information contribute to this effect, as we |
---|
1047 | illustrate at the example of SPL in Fig.~\ref{fig:degeneracies_SPL}. |
---|
1048 | The dashed curves in the left panel of this figure show the allowed |
---|
1049 | regions for only the appearance measurement (for neutrinos and |
---|
1050 | antineutrinos) without spectral information, i.e., just a counting |
---|
1051 | experiment. In this case the eight-fold degeneracy is present in its |
---|
1052 | full beauty, and one finds two solutions (corresponding to the |
---|
1053 | intrinsic degeneracy) for each choice of sign($\Delta m^2_{31}$) and |
---|
1054 | the octant of $\theta_{23}$. Moreover, the allowed regions are |
---|
1055 | relatively large. For the thin solid curves the information from the |
---|
1056 | disappearance rate is added. The main effect is to decrease the size |
---|
1057 | of the allowed regions in $\stheta$. This is especially pronounced for |
---|
1058 | the solutions involving the wrong octant of $\theta_{23}$, since these |
---|
1059 | solutions are strongly affected by an uncertainty in $\theta_{23}$ |
---|
1060 | which gets reduced by the disappearance information. Using in addition |
---|
1061 | to the disappearance rate also the spectrum again decreases the size |
---|
1062 | of the allowed regions, however, still all eight solutions are present |
---|
1063 | (compare dashed curves in the right panel). |
---|
1064 | % |
---|
1065 | The most relevant effect comes from the inclusion of spectral |
---|
1066 | information in the appearance channel, as visible from the comparison |
---|
1067 | of the dashed and thick-solid curves in the right panel of |
---|
1068 | Fig.~\ref{fig:degeneracies_SPL}. The intrinsic degeneracy gets |
---|
1069 | resolved and only four solutions corresponding to the sign and octant |
---|
1070 | degeneracies are left (see, e.g., |
---|
1071 | Refs.~\cite{Huber:2002mx,Huber:2005ep,Ishitsuka:2005qi}).\footnote{The |
---|
1072 | inclusion of spectral information might be the source of possible |
---|
1073 | differences to previous studies, see e.g.\ Ref.~\cite{Donini:2004hu}.} |
---|
1074 | Note that the thick curves in the right panel of |
---|
1075 | Fig.~\ref{fig:degeneracies_SPL} correspond to the regions show in |
---|
1076 | Fig.~\ref{fig:degeneracies} for the SPL. |
---|
1077 | % |
---|
1078 | Finally, by the inclusion of information from atmospheric neutrinos |
---|
1079 | all degeneracies can be resolved in this example, and the true |
---|
1080 | solution is identified at 95\%~CL (see Sec.~\ref{sec:atmospherics} and |
---|
1081 | Ref.~\cite{Huber:2005ep} for further discussions of atmospheric |
---|
1082 | neutrinos). |
---|
1083 | |
---|
1084 | Concerning the \BB\ one observes from Fig.~\ref{fig:degeneracies} that |
---|
1085 | in this case the ($\delCP,\theta_{13}$)-degeneracy cannot be resolved |
---|
1086 | and one has to deal with eight distinct solutions. One reason for this |
---|
1087 | is the absence of precise information on $|\Delta m^2_{31}|$ and |
---|
1088 | $\sin^22\theta_{23}$ which is provided by the $\nu_\mu$ disappearance |
---|
1089 | in Super Beam experiments but is not available from the \BB. If |
---|
1090 | external information on these parameters at the level of 3\% is |
---|
1091 | included the allowed regions in Fig.~\ref{fig:degeneracies} are |
---|
1092 | significantly reduced. However, still all eight solutions are present, |
---|
1093 | which indicates that for the \BB\ spectral information is not |
---|
1094 | efficient enough to resolve the ($\delCP,\theta_{13}$)-degeneracy, and |
---|
1095 | in this case only the inclusion of atmospheric neutrino data allows a |
---|
1096 | nearly complete resolution of the degeneracies. |
---|
1097 | |
---|
1098 | An important observation from Fig.~\ref{fig:degeneracies} is that |
---|
1099 | degeneracies have only a very small impact on the CP violation |
---|
1100 | discovery, in the sense that if the true solution is CP violating also |
---|
1101 | the fake solutions are located at CP violating values of |
---|
1102 | $\delCP$. Indeed, since for the relatively short baselines in the |
---|
1103 | experiments under consideration matter effects are very small, the |
---|
1104 | sign($\Delta m^2_{31}$)-degenerate solution is located within good |
---|
1105 | approximation at $\delCP' \approx \pi - |
---|
1106 | \delCP$~\cite{Minakata:2001qm}. Therefore, although degeneracies |
---|
1107 | strongly affect the determination of $\theta_{13}$ and $\delCP$ they |
---|
1108 | have only a small impact on the CP violation discovery potential. |
---|
1109 | Furthermore, as clear from Fig.~\ref{fig:degeneracies} the sign($\Delta |
---|
1110 | m^2_{31}$) degeneracy has practically no effect on the $\theta_{13}$ |
---|
1111 | measurement, whereas the octant degeneracy has very little impact on |
---|
1112 | the determination of $\delCP$. |
---|
1113 | |
---|
1114 | \begin{figure}[!t] |
---|
1115 | \centering |
---|
1116 | \includegraphics[width=0.9\textwidth]{./fig7.eps} |
---|
1117 | % |
---|
1118 | \mycaption{Allowed regions in $\sin^22\theta_{13}$ and |
---|
1119 | $\delta_\mathrm{CP}$ for 5~years data (neutrinos only) from \BB, |
---|
1120 | SPL, and the combination. $\mathrm{H^{tr/wr} (O^{tr/wr})}$ refers to |
---|
1121 | solutions with the true/wrong mass hierarchy (octant of |
---|
1122 | $\theta_{23}$). For the colored regions in the left panel also |
---|
1123 | 5~years of atmospheric data are included; the solution with the |
---|
1124 | wrong hierarchy has $\Delta\chi^2 = 4$. The true parameter |
---|
1125 | values are $\delta_\mathrm{CP} = -0.85 \pi$, $\sin^22\theta_{13} = |
---|
1126 | 0.03$, $\sin^2\theta_{23} = 0.6$, and the values from |
---|
1127 | Eq.~(\ref{eq:default-params}) for the other parameters. For the \BB\ |
---|
1128 | only analysis (middle panel) an external accuracy of 2\% (3\%) for |
---|
1129 | $|\Delta m^2_{31}|$ ($\theta_{23}$) has been assumed, whereas for |
---|
1130 | the left and right panel the default value of 10\% has been used.} |
---|
1131 | \label{fig:degeneracies_5yrs} |
---|
1132 | \end{figure} |
---|
1133 | |
---|
1134 | Fig.~\ref{fig:degeneracies} shows also that the fake solutions occur |
---|
1135 | at similar locations in the ($\stheta$, $\delCP$) plane for \BB\ and |
---|
1136 | SPL. Therefore, as noted in Ref.~\cite{Donini:2004hu}, in this sense |
---|
1137 | the two experiments are not complementary, and the combination of |
---|
1138 | 10~years of \BB\ and SPL data is not very effective in resolving |
---|
1139 | degeneracies. This is obvious since the baseline is the same and the |
---|
1140 | neutrino energies are similar. |
---|
1141 | % |
---|
1142 | Note however, that the \BB\ looks for $\nu_e\to\nu_\mu$ appearance, |
---|
1143 | whereas in SPL the T-conjugate channel $\nu_\mu\to\nu_e$ is observed. |
---|
1144 | Assuming CPT invariance the relation $P_{\nu_\alpha\to\nu_\beta} = |
---|
1145 | P_{\bar\nu_\beta\to\bar\nu_\alpha}$ holds, which implies that the |
---|
1146 | antineutrino measurement can be replaced by a measurement in the |
---|
1147 | T-conjugate channel. Hence, if \BB\ and SPL experiments are available |
---|
1148 | simultaneously the full information can be obtained just from neutrino |
---|
1149 | data, and in principle the (time consuming) antineutrino measurement |
---|
1150 | is not necessary. As shown in Fig.~\ref{fig:degeneracies_5yrs} the |
---|
1151 | combination of 5~yrs neutrino data from the \BB\ with 5~yrs of |
---|
1152 | neutrino data from SPL leads to a result very close to the 10~yrs |
---|
1153 | neutrino+antineutrino data from one experiment alone. Hence, if \BB\ |
---|
1154 | and SPL experiments are available simultaneously the data taking |
---|
1155 | period is reduced approximately by a factor of 2 with respect to a |
---|
1156 | single experiment. This synergy is discussed later in |
---|
1157 | Sec.~\ref{sec:synergies-beams} in the context of the $\theta_{13}$ and |
---|
1158 | CP violation discovery potentials. |
---|
1159 | |
---|
1160 | |
---|
1161 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1162 | \section{Physics potential} |
---|
1163 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1164 | \label{sec:sensitivities} |
---|
1165 | |
---|
1166 | \subsection{Sensitivity to the atmospheric parameters} |
---|
1167 | \label{sec:atm} |
---|
1168 | |
---|
1169 | The $\nu_\mu$ disappearance channel available in the Super Beam |
---|
1170 | experiments SPL and T2HK allows a precise determination of the |
---|
1171 | atmospheric parameters $|\Delta m^2_{31}|$ and $\sin^22\theta_{23}$, |
---|
1172 | see, e.g., Refs.~\cite{Antusch:2004yx,Minakata:2004pg,Donini:2005db} |
---|
1173 | for recent analyses). Fig.~\ref{fig:atm-params} illustrates the |
---|
1174 | improvement on these parameters by Super Beam experiments with respect |
---|
1175 | to the present knowledge from SK atmospheric and K2K data. We show the |
---|
1176 | allowed regions at 99\%~CL for T2K-I, SPL, and T2HK, where in all |
---|
1177 | three cases 5~years of neutrino data are assumed. T2K-I corresponds to |
---|
1178 | the phase~I of the T2K experiment with a beam power of 0.77~MW and the |
---|
1179 | Super-Kamiokande detector as target~\cite{T2K}. In Tab.~\ref{tab:atm-params} we |
---|
1180 | give the corresponding relative accuracies at 3$\sigma$ for $|\Delta |
---|
1181 | m^2_{31}|$ and $\sin^2\theta_{23}$. |
---|
1182 | |
---|
1183 | \begin{figure}[!t] |
---|
1184 | \centering |
---|
1185 | \includegraphics[width=0.55\textwidth]{./fig8.eps} |
---|
1186 | \mycaption{\label{fig:atm-params} Allowed regions of $\Delta |
---|
1187 | m^2_{31}$ and $\sin^2\theta_{23}$ at 99\%~CL (2 d.o.f.) after 5~yrs |
---|
1188 | of neutrino data taking for SPL, T2K phase~I, T2HK, and the |
---|
1189 | combination of SPL with 5~yrs of atmospheric neutrino data in the |
---|
1190 | MEMPHYS detector. For the true parameter values we use $\Delta |
---|
1191 | m^2_{31} = 2.2\, (2.6) \times 10^{-3}~\mathrm{eV}^2$ and |
---|
1192 | $\sin^2\theta_{23} = 0.5 \, (0.37)$ for the test point 1 (2), and |
---|
1193 | $\theta_{13} = 0$ and the solar parameters as given in |
---|
1194 | Eq.~(\ref{eq:default-params}). The shaded region corresponds to the |
---|
1195 | 99\%~CL region from present SK and K2K data~\cite{Maltoni:2004ei}.} |
---|
1196 | \end{figure} |
---|
1197 | |
---|
1198 | |
---|
1199 | \begin{table}[!t] |
---|
1200 | \centering |
---|
1201 | \begin{tabular}{lcrrr} |
---|
1202 | \hline\noalign{\smallskip} |
---|
1203 | & True values & T2K-I & SPL & T2HK \\ |
---|
1204 | \noalign{\smallskip}\hline\noalign{\smallskip} |
---|
1205 | $\Delta m^2_{31}$ & $2.2\cdot 10^{-3}$ eV$^2$ & 4.7\% & 3.2\% & 1.1\% \\ |
---|
1206 | $\sin^2\theta_{23}$ & $0.5$ & 20\% & 20\% & 6\% \\ |
---|
1207 | \noalign{\smallskip}\hline\noalign{\smallskip} |
---|
1208 | $\Delta m^2_{31}$ & $2.6\cdot 10^{-3}$ eV$^2$ & 4.4\% & 2.5\% & 0.7\% \\ |
---|
1209 | $\sin^2\theta_{23}$ & $0.37$ & 8.9\% & 3.1\% & 0.8\% \\ |
---|
1210 | \noalign{\smallskip}\hline |
---|
1211 | \end{tabular} |
---|
1212 | \mycaption{Accuracies at $3\sigma$ on the atmospheric parameters |
---|
1213 | $|\Delta m^2_{31}|$ and $\sin^2\theta_{23}$ for 5 years of neutrino |
---|
1214 | data from T2K-I, SPL, and T2HK for the two test points shown in |
---|
1215 | Fig.~\ref{fig:atm-params} ($\theta^\mathrm{true}_{13} = 0$). The |
---|
1216 | accuracy for a parameter $x$ is defined as $(x^\mathrm{upper} - |
---|
1217 | x^\mathrm{lower})/(2 x^\mathrm{true})$, where $x^\mathrm{upper}$ |
---|
1218 | ($x^\mathrm{lower}$) is the upper (lower) bound at 3$\sigma$ for |
---|
1219 | 1~d.o.f.\ obtained by projecting the contour $\Delta \chi^2 = 9$ |
---|
1220 | onto the $x$-axis. For the accuracies for test point~2 the octant |
---|
1221 | degenerate solution is neglected.\label{tab:atm-params}} |
---|
1222 | \end{table} |
---|
1223 | |
---|
1224 | From the figure and the table it becomes evident that the T2K setups |
---|
1225 | are very good in measuring the atmospheric parameters, and only a |
---|
1226 | modest improvement is possible with SPL with respect to T2K phase~I. |
---|
1227 | T2HK provides an excellent sensitivity for these parameters, and for |
---|
1228 | the example of the test point~2 sub-percent accuracies are obtained at |
---|
1229 | 3$\sigma$. The disadvantage of SPL with respect to T2HK is the |
---|
1230 | limited spectral information. Because of the lower beam energy |
---|
1231 | nuclear Fermi motion is a severe limitation for energy reconstruction |
---|
1232 | in SPL, whereas in T2K the somewhat higher energy allows an efficient |
---|
1233 | use of spectral information of quasi-elastic events. Indeed, due to |
---|
1234 | the large number of events in the disappearance channel (cf.\ |
---|
1235 | Tab.~\ref{tab:events}) the measurement is completely dominated by the |
---|
1236 | spectrum, and even increasing the normalization uncertainty up to |
---|
1237 | 100\% has very little impact on the allowed regions. The effect of |
---|
1238 | spectral information on the disappearance measurement is |
---|
1239 | discussed in some detail in Ref.~\cite{Donini:2005db}. |
---|
1240 | |
---|
1241 | In the interpretation of the numbers given in |
---|
1242 | Tab.~\ref{tab:atm-params} one should consider that at accuracies below |
---|
1243 | 1\% systematics might become important, which are not accounted for |
---|
1244 | here. We do include the most relevant systematics (see |
---|
1245 | Secs.~\ref{sec:analysis} and \ref{sec:experiments}), however, at that |
---|
1246 | level additional uncertainties related to, for example, the spectral |
---|
1247 | shapes of signal and/or background, or the energy calibration might |
---|
1248 | eventually limit the accuracy. |
---|
1249 | |
---|
1250 | For the test point~1, with maximal mixing for $\theta_{23}$, rather |
---|
1251 | poor accuracies of $\sim20\%$ for T2K-I and SPL, and $6\%$ for T2HK |
---|
1252 | are obtained for $\sin^2\theta_{23}$. The reason is that in the |
---|
1253 | disappearance channel $\sin^22\theta_{23}$ is measured with high |
---|
1254 | precision, which translates to rather large errors for |
---|
1255 | $\sin^2\theta_{23}$ if $\theta_{23} = \pi/4$~\cite{Minakata:2004pg}. |
---|
1256 | % |
---|
1257 | For the same reason it is difficult to resolve the octant degeneracy, |
---|
1258 | and for the test point~2, with a non-maximal value of |
---|
1259 | $\sin^2\theta_{23} = 0.37$, for all three LBL experiments the |
---|
1260 | degenerate solution is present around $\sin^2\theta_{23} = 0.63$. |
---|
1261 | % |
---|
1262 | As pointed out in Refs.~\cite{Peres:2003wd,Gonzalez-Garcia:2004cu} |
---|
1263 | atmospheric neutrino data may allow to distinguish between the two |
---|
1264 | octants of $\theta_{23}$. If 5~years of atmospheric neutrino data in |
---|
1265 | MEMPHYS are added to the SPL data, the degenerate solution for the |
---|
1266 | test point~2 can be excluded at more than $5\sigma$ and hence the |
---|
1267 | octant degeneracy is resolved in this example, see |
---|
1268 | Sec.~\ref{sec:atmospherics} for a more detailed discussion. |
---|
1269 | |
---|
1270 | |
---|
1271 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1272 | \subsection{The $\theta_{13}$ discovery potential} |
---|
1273 | \label{sec:th13} |
---|
1274 | |
---|
1275 | If no finite value of $\theta_{13}$ is discovered by the next round of |
---|
1276 | experiments an important task of the experiments under consideration |
---|
1277 | here is to push further the sensitivity to this parameter. In this |
---|
1278 | section we address this problem, where we use to following definition |
---|
1279 | of the $\theta_{13}$ discovery potential: Data are simulated for a |
---|
1280 | finite true value of $\stheta$ and a given true value for $\delCP$. If |
---|
1281 | the $\Delta\chi^2$ of the fit to these data with $\theta_{13} = 0$ is |
---|
1282 | larger than 9 the corresponding true value of $\theta_{13}$ ``is |
---|
1283 | discovered at 3$\sigma$''. In other words, the $3\sigma$ discovery |
---|
1284 | limit as a function of the true $\delCP$ is given by the true value of |
---|
1285 | $\stheta$ for which $\Delta\chi^2(\theta_{13}=0) = 9$. In the fitting |
---|
1286 | process we minimize the $\Delta\chi^2$ with respect to $\theta_{12}$, |
---|
1287 | $\theta_{23}$, $\Delta m^2_{12}$, and $\Delta m^2_{31}$, and in |
---|
1288 | general one has to test also for degenerate solutions in sign($\Delta |
---|
1289 | m^2_{31}$) and the octant of $\theta_{23}$. |
---|
1290 | |
---|
1291 | \begin{figure} |
---|
1292 | \centering \includegraphics[width=0.9\textwidth]{./fig9.eps} |
---|
1293 | \mycaption{$3\sigma$ discovery sensitivity to $\stheta$ for \BB, |
---|
1294 | SPL, and T2HK as a function of the true value of \delCP\ (left |
---|
1295 | panel) and as a function of the fraction of all possible values of |
---|
1296 | \delCP\ (right panel). The running time is ($5\nu + 5\bar\nu$)~yrs |
---|
1297 | for \BB\ and ($2\nu + 8\bar\nu$)~yrs for the Super Beams. The width |
---|
1298 | of the bands corresponds to values for the systematical errors |
---|
1299 | between 2\% and 5\%. The black curves correspond to the combination |
---|
1300 | of \BB\ and SPL with 10~yrs of total data taking each for a |
---|
1301 | systematical error of 2\%, and the dashed curves show the |
---|
1302 | sensitivity of the \BB\ when the number of ion decays/yr are reduced |
---|
1303 | by a factor of two with respect to the values given in |
---|
1304 | Tab.~\ref{tab:setups}.\label{fig:th13}} |
---|
1305 | \end{figure} |
---|
1306 | |
---|
1307 | The discovery limits are shown for \BB, SPL, and T2HK in |
---|
1308 | Fig.~\ref{fig:th13}. One observes that SPL and T2HK are rather similar |
---|
1309 | in performance, whereas the \BB\ with our standard fluxes performs |
---|
1310 | significantly better. For all three facilities a guaranteed discovery |
---|
1311 | reach of $\stheta \simeq 5\times 10^{-3}$ is obtained, irrespective of |
---|
1312 | the actual value of \delCP, however, for certain values of \delCP\ the |
---|
1313 | sensitivity is significantly improved. For SPL and T2HK discovery |
---|
1314 | limits around $\stheta \simeq 10^{-3}$ are possible for a large |
---|
1315 | fraction of all possible values of \delCP, whereas for our standard |
---|
1316 | \BB\ a sensitivity below $\stheta = 4\times 10^{-4}$ is reached for |
---|
1317 | 80\% of all possible values of \delCP. If 10~years of data from \BB\ |
---|
1318 | and SPL are combined the discovery limit is dominated by the \BB. |
---|
1319 | % |
---|
1320 | Let us stress that the \BB\ performance depends crucially on the |
---|
1321 | neutrino flux intensity, as can be seen from the dashed curves in |
---|
1322 | Fig.~\ref{fig:th13}, which has been obtained by reducing the number of |
---|
1323 | ion decays/yr by a factor of two with respect to our standard values |
---|
1324 | given in Tab.~\ref{tab:setups}. In this case the sensitivity decreases |
---|
1325 | significantly, but still values slightly better than from the |
---|
1326 | Super Beam experiments are reached. |
---|
1327 | |
---|
1328 | The peak of the sensitivity curves around $\delCP \approx \pi$ appears |
---|
1329 | due to the interplay of neutrino and antineutrino data. For the Super |
---|
1330 | Beams neutrino (antineutrino) data are most sensitive in the region |
---|
1331 | $\pi \lesssim \delCP \lesssim 2\pi$ ($0 \lesssim \delCP \lesssim |
---|
1332 | \pi$), and opposite for the \BB, compare also Fig.~\ref{fig:th13-5yrs} |
---|
1333 | in Sec.~\ref{sec:synergies-beams}. The particular shape of the |
---|
1334 | sensitivity curves emerges from the relative location of the |
---|
1335 | corresponding curves for neutrino and antineutrino data, which is |
---|
1336 | controlled by the $L/E_\nu$ value where the experiment is operated and |
---|
1337 | the value of $|\Delta m^2_{31}|$. The fact that the peak is most |
---|
1338 | pronounced for the \BB\ follows from the somewhat smaler $L/E_\nu$ of |
---|
1339 | the \BB\ compared to the Super Beams, whereas the shapes for SPL and |
---|
1340 | T2HK are similar because of the similar $L/E_\nu$ values. |
---|
1341 | |
---|
1342 | In Fig.~\ref{fig:th13} we illustrate also the effect of systematical |
---|
1343 | errors on the $\theta_{13}$ discovery reach. The lower boundary of the |
---|
1344 | band for each experiment corresponds to a systematical error of 2\%, |
---|
1345 | whereas the upper boundary is obtained for 5\%. These errors include |
---|
1346 | the (uncorrelated) normalization uncertainties on the signal as well |
---|
1347 | as on the background, where the crucial uncertainty is the error on |
---|
1348 | the background. We find that the \BB\ is basically not affected by |
---|
1349 | these errors, since the background has a rather different spectral |
---|
1350 | shape (strongly peaked at low energies) than the signal. The fact |
---|
1351 | that T2HK is relatively strongly affected by the actual value of the |
---|
1352 | systematics can by understood by considering the ratio of signal to |
---|
1353 | the square-root of the background using the numbers of |
---|
1354 | Tab.~\ref{tab:events}. We shall discuss this issue in more detail in |
---|
1355 | the next section in the context of the CP violation discovery reach. |
---|
1356 | |
---|
1357 | \begin{figure} |
---|
1358 | \centering \includegraphics[width=0.9\textwidth]{./fig10.eps} |
---|
1359 | \mycaption{\label{fig:SPLTheta13Disco} $3\sigma$ discovery |
---|
1360 | sensitivity to $\stheta$ for the SPL as a function of the true value |
---|
1361 | of \delCP\ for $\sin^2\theta_{23}^\mathrm{true} = 0.6$ and true |
---|
1362 | values for the other parameters as given in |
---|
1363 | Eq.~(\ref{eq:default-params}). The running time is ($2\nu + |
---|
1364 | 8\bar\nu$)~yrs. |
---|
1365 | } |
---|
1366 | \end{figure} |
---|
1367 | |
---|
1368 | Let us remark that the $\theta_{13}$ sensitivities are practically not |
---|
1369 | affected by the sign($\Delta m^2_{31}$)-degeneracy. This is easy to |
---|
1370 | understand, since the data is fitted with $\theta_{13} = 0$, and in |
---|
1371 | this case both mass hierarchies lead to very similar event rates. If |
---|
1372 | the inverted hierarchy is used as the true hierarchy, the peak in the |
---|
1373 | discovery limit visible in the left panel of Fig.~\ref{fig:th13} |
---|
1374 | around $\delCP \sim \pi$ moves to $\delCP \sim 0$. However, the |
---|
1375 | characteristic shape of the curves, and in particular, the sensitivity |
---|
1376 | as a function of the \delCP-fraction shown in the right panel are |
---|
1377 | hardly affected by the sign of the true $\Delta m^2_{31}$. |
---|
1378 | % |
---|
1379 | In case of a non-maximal value of $\theta_{23}$ the octant-degeneracy |
---|
1380 | has a minor impact on the $\theta_{13}$ discovery potential, as |
---|
1381 | illustrated in Fig.~\ref{fig:SPLTheta13Disco} for the SPL. We show the |
---|
1382 | discovery limit obtained with the true and the fake octant of |
---|
1383 | $\theta_{23}$ for a true value of $\sin^2\theta_{23}= 0.6$. Let us |
---|
1384 | note that for true values of $\sin^2\theta_{23} > 0.5$ the |
---|
1385 | octant-degenerate solution leads to a worse sensitivity to |
---|
1386 | $\theta_{13}$ (see figure), whereas for $\sin^2\theta_{23} < 0.5$ the |
---|
1387 | fake solution does not affect the $\theta_{13}$ discovery, since in |
---|
1388 | this case the sensitivity is increased. |
---|
1389 | |
---|
1390 | |
---|
1391 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1392 | \subsection{Sensitivity to CP violation} |
---|
1393 | \label{sec:CPV} |
---|
1394 | |
---|
1395 | In case a finite value of $\theta_{13}$ is established it is important |
---|
1396 | to quantitatively assess the discovery potential for leptonic CP |
---|
1397 | violation (CPV). The CP symmetry is violated if the complex phase |
---|
1398 | \delCP\ is different from $0$ and $\pi$. Therefore, CPV is discovered |
---|
1399 | if these values for \delCP\ can be excluded. |
---|
1400 | % |
---|
1401 | We evaluate the discovery potential for CPV in the following way: |
---|
1402 | Data are calculated by scanning the true values of $\stheta$ and |
---|
1403 | $\delCP$. Then these data are fitted with the CP conserving values |
---|
1404 | $\delCP = 0$ and $\delCP = \pi$, where all parameters except \delCP\ |
---|
1405 | are varied and the sign and octant degeneracies are taken into |
---|
1406 | account. If no fit with $\Delta \chi^2 < 9$ is found CP conserving |
---|
1407 | values of \delCP\ can be excluded at $3\sigma$ for the chosen values |
---|
1408 | of $\delta_\mathrm{CP}^\mathrm{true}$ and $\stheta^\mathrm{true}$. |
---|
1409 | |
---|
1410 | \begin{figure}[!t] |
---|
1411 | \centering |
---|
1412 | \includegraphics[width=0.65\textwidth]{./fig11.eps} |
---|
1413 | % |
---|
1414 | \mycaption{CPV discovery potential for \BB, SPL, and T2HK: For |
---|
1415 | parameter values inside the ellipse-shaped curves CP conserving |
---|
1416 | values of \delCP\ can be excluded at $3\sigma$ $(\Delta\chi^2>9)$. |
---|
1417 | The running time is ($5\nu + 5\bar\nu$)~yrs for \BB\ and ($2\nu + |
---|
1418 | 8\bar\nu$)~yrs for the Super Beams. The width of the bands |
---|
1419 | corresponds to values for the systematical errors from 2\% to |
---|
1420 | 5\%. The dashed curves show the sensitivity of the \BB\ when the |
---|
1421 | number of ion decays/yr are reduced by a factor of two with respect |
---|
1422 | to the values given in Tab.~\ref{tab:setups} for 2\% |
---|
1423 | systematics.\label{fig:CPV}} |
---|
1424 | \end{figure} |
---|
1425 | |
---|
1426 | The CPV discovery potential for \BB, SPL, and T2HK is shown in |
---|
1427 | Fig.~\ref{fig:CPV}. As in the case of the $\theta_{13}$ sensitivity we |
---|
1428 | find that SPL and T2HK perform rather similar, whereas the \BB\ has |
---|
1429 | significantly better sensitivity if our adopted numbers of ion decays |
---|
1430 | per year can be achieved. For systematical errors of 2\% maximal CPV |
---|
1431 | (for $\delCP^\mathrm{true} = \pi/2, \, 3\pi/2$) can be discovered at |
---|
1432 | $3\sigma$ down to $\stheta \simeq 8.8 \,(6.6)\times 10^{-4}$ for SPL |
---|
1433 | (T2HK), and $\stheta \simeq 2\times 10^{-4}$ for the \BB. This number |
---|
1434 | for the \BB\ is increased by a factor 3 if the fluxes are reduced to |
---|
1435 | half of our nominal values. The best sensitivity to CPV is obtained |
---|
1436 | for all three facilities around $\stheta \sim 10^{-2}$. For this value |
---|
1437 | CPV can be established for 78\%, 73\%, 75\% of all values of \delCP\ |
---|
1438 | for \BB, SPL, T2HK, respectively (again for systematics of 2\%). |
---|
1439 | |
---|
1440 | The widths of the bands in Fig.~\ref{fig:CPV} corresponds to different |
---|
1441 | values for systematical errors. The curves which give the best |
---|
1442 | sensitivities are obtained for systematics of 2\%, the curves |
---|
1443 | corresponding to the worst sensitivity have been computed for |
---|
1444 | systematics of 5\%. We change the uncertainty on the signal as well as |
---|
1445 | on the background, however, it turns out that the most relevant |
---|
1446 | uncertainty is the background normalization. We find that the impact |
---|
1447 | of systematics is very small for the \BB. The reason for this is that |
---|
1448 | the spectral shape of the background in the \BB\ (from pions and |
---|
1449 | atmospheric neutrinos) is very different from the signal, and |
---|
1450 | therefore they can be disentangled by the fit of the energy spectrum. |
---|
1451 | For the Super Beams the background spectrum is more similar to the |
---|
1452 | signal, and therefore an uncertainty on the background normalization |
---|
1453 | might have a strong impact on the sensitivity, as visible from the SPL |
---|
1454 | and T2HK curves in Fig.~\ref{fig:CPV}. In particular T2HK is strongly |
---|
1455 | affected, and moving from 2\% to 5\% uncertainy decreases the |
---|
1456 | sensitivity to maximal CPV by a factor 3. |
---|
1457 | |
---|
1458 | \begin{figure}[!t] |
---|
1459 | \centering |
---|
1460 | \includegraphics[width=0.9\textwidth]{./fig12.eps} |
---|
1461 | % |
---|
1462 | \mycaption{Impact of total exposure and systematical errors on the |
---|
1463 | CPV discovery potential of \BB, SPL, and T2HK. We show the |
---|
1464 | smallest true value of $\stheta$ for which $\delCP = \pi/2$ can be |
---|
1465 | distinguished from $\delCP = 0$ or $\delCP = \pi$ at $3\sigma$ |
---|
1466 | $(\Delta\chi^2>9)$ as a function of the exposure in kt~yrs (left) |
---|
1467 | and as a function of the systematical error on the background |
---|
1468 | $\sigma_\mathrm{bkgr}$ (right). The widths of the curves in the |
---|
1469 | left panel corresponds to values of $\sigma_\mathrm{bkgr}$ from 2\% |
---|
1470 | to 5\%. The thin solid curves in the left panel corresponds to no |
---|
1471 | systematical errors. The right plot is calculated for the standard |
---|
1472 | exposure of 4400~kt~yrs. No systematical error on the signal has |
---|
1473 | been assumed. \label{fig:systematics}} |
---|
1474 | \end{figure} |
---|
1475 | |
---|
1476 | This interesting feature can be understood in the following way. A |
---|
1477 | rough measure to estimate the sensitivity is given by the signal |
---|
1478 | compared to the error on the background. The latter receives |
---|
1479 | contributions from the statistical error $\sqrt{B}$ and from the |
---|
1480 | systematical uncertainty $\sigma_\mathrm{bkgr}B$, where $B$ is the |
---|
1481 | number of background events and $\sigma_\mathrm{bkgr}$ is the |
---|
1482 | (relative) systematical error. Hence the importance of the systematics |
---|
1483 | can be estimated by the ratio of systematical and statistical errors |
---|
1484 | $\sigma_\mathrm{bkgr} B / \sqrt{B} = \sigma_\mathrm{bkgr} \sqrt{B}$. |
---|
1485 | Summing the numbers for background events in the neutrino and |
---|
1486 | antineutrino channels given in Tab.~\ref{tab:events} one finds that |
---|
1487 | systematical errors dominate ($\sigma_\mathrm{bkgr} \sqrt{B} > 1$) if |
---|
1488 | $\sigma_\mathrm{bkgr} \gtrsim 6\%,\, 3\%, \, 2\%$ for \BB, SPL, T2HK, |
---|
1489 | respectively. |
---|
1490 | % |
---|
1491 | In the right panel Fig.~\ref{fig:systematics} we show the sensitivity |
---|
1492 | to maximal CPV (as defined in the figure caption) as a function of |
---|
1493 | $\sigma_\mathrm{bkgr}$. Indeed, the worsening of the sensitivity due |
---|
1494 | to systematics occurs roughly at the values of $\sigma_\mathrm{bkgr}$ |
---|
1495 | as estimated above. For a more quantitative understanding of these |
---|
1496 | curves it is necessary to consider the number of signal and background |
---|
1497 | events for neutrinos and antineutrinos separately, as well as to take |
---|
1498 | into account spectral information. |
---|
1499 | |
---|
1500 | |
---|
1501 | The left panel of Fig.~\ref{fig:systematics} shows the sensitivity to |
---|
1502 | maximal CPV as a function of the exposure\footnote{Note that the CPV |
---|
1503 | sensitivity for the \BB\ with reduced fluxes from Fig.~\ref{fig:CPV} |
---|
1504 | is worse than the value which follows from Fig.~\ref{fig:systematics}. |
---|
1505 | The reason is that in Fig.~\ref{fig:systematics} the total exposure is |
---|
1506 | scaled (mass~$\times$~time), i.e., signal and background are scaled in |
---|
1507 | the same way, whereas for the dashed curve in Fig.~\ref{fig:CPV} only |
---|
1508 | the fluxes are reduced but backgrounds are kept constant.} for values |
---|
1509 | of $\sigma_\mathrm{bkgr}$ from 2\% to 5\%. One can observe clearly |
---|
1510 | that for the standard exposure of 4400~kt~yrs T2HK is dominated by |
---|
1511 | systematics and changing $\sigma_\mathrm{bkgr}$ from 2\% to 5\% has a |
---|
1512 | big impact on the sensitivity. In contrast the CERN--MEMPHYS |
---|
1513 | experiments (especially the \BB) are rather stable with respect to |
---|
1514 | systematics and for the standard exposure they are still statistics |
---|
1515 | dominated. We conclude that in T2HK systematics have to be under very |
---|
1516 | good control, whereas this issue is less important for \BB\ and SPL. |
---|
1517 | % |
---|
1518 | We have checked explicitly that the systematical error on the signal |
---|
1519 | has negligible impact on these results. Therefore, we have set this |
---|
1520 | error to zero for calculating Fig.~\ref{fig:systematics} to highlight |
---|
1521 | the importance of the background error. In all other calculations also |
---|
1522 | the signal error is included, in particular also in Fig.~\ref{fig:CPV}. |
---|
1523 | |
---|
1524 | Let us remark that for the T2KK configuration (with one half of the |
---|
1525 | Hyper-K detector mass at Kamioka and the second half at the same |
---|
1526 | off-axis angle in Korea) the problem of systematics might be less |
---|
1527 | severe than for T2HK, since both detectors observe the same flux and |
---|
1528 | background. |
---|
1529 | % |
---|
1530 | Note however, that an important issue for the CPV sensitivity is |
---|
1531 | whether systematics between neutrino and antineutrino data are |
---|
1532 | correlated or not. We have checked that the worse sensitivies for T2HK |
---|
1533 | shown in Fig.~\ref{fig:CPV} compared to the results obtained in |
---|
1534 | Refs.~\cite{Ishitsuka:2005qi,Kajita:2006bt} can be traced back to the |
---|
1535 | fact that in these papers neutrino and antineutrino systematics are |
---|
1536 | correlated, whereas we consider them to be independent. Note that our |
---|
1537 | approach is conservative, and the assumption of uncorrelated errors |
---|
1538 | has been adopted also for the CERN--MEMPHYS experiments. |
---|
1539 | |
---|
1540 | |
---|
1541 | \begin{figure}[!t] |
---|
1542 | \centering |
---|
1543 | \includegraphics[width=0.8\textwidth]{./fig13.eps} |
---|
1544 | % |
---|
1545 | \mycaption{Impact of degeneracies on the CPV discovery potential |
---|
1546 | for the \BB. We show the sensitivity to CPV at $3\sigma$ |
---|
1547 | $(\Delta\chi^2>9)$ computed for 4 different combinations of the |
---|
1548 | true values of the hierarchy (NH or IH) and $\theta_{23}$ |
---|
1549 | ($\sin^2\theta_{23} = 0.4$ or $0.6$). Dashed curves are computed |
---|
1550 | neglecting degeneracies in the fit. The running time is ($5\nu + |
---|
1551 | 5\bar\nu$)~yrs. |
---|
1552 | \label{fig:deltacp}} |
---|
1553 | \end{figure} |
---|
1554 | |
---|
1555 | Finally, in Fig.~\ref{fig:deltacp} we illustrate the impact of |
---|
1556 | degeneracies, as well as the true hierarchy and \thetatt-octant on the |
---|
1557 | CPV sensitivity. Curves of different colors correspond to the four |
---|
1558 | different choices for \sigdm\ and the \thetatt-octant of the true |
---|
1559 | parameters. For the solid curves the simulated data for each choice of |
---|
1560 | true \sigdm\ and \thetatt-octant are fitted by taking into account all |
---|
1561 | four degenerate solutions, i.e., also for the fit all four |
---|
1562 | combinations of \sigdm\ and \thetatt-octant are used. One observes |
---|
1563 | from the figure that the true hierarchy and octant have a rather small |
---|
1564 | impact on the \BB\ CPV sensitivity, in particular the sensitivity to |
---|
1565 | maximal CPV is completely independent. The main effect of changing the |
---|
1566 | true hierarchy is to exchange the behavior between $0 < \delCP < |
---|
1567 | 180^\circ$ and $180^\circ < \delCP < 360^\circ$. For $\stheta \lesssim |
---|
1568 | 10^{-2}$ the sensitivity gets slightly worse if |
---|
1569 | $\thetatt^\mathrm{true} > \pi/4$ compared to $\thetatt^\mathrm{true} < |
---|
1570 | \pi/4$. |
---|
1571 | |
---|
1572 | The dashed curves in Fig.~\ref{fig:deltacp} are computed without |
---|
1573 | taking into account the degeneracies, i.e., for each choice of true |
---|
1574 | \sigdm\ and \thetatt-octant the data are fitted only with this |
---|
1575 | particular choice. The effect of the degeneracies becomes visible for |
---|
1576 | large values of \thetaot. Note that this is just the region where they |
---|
1577 | can be reduced by a combined analysis with atmospheric neutrinos (see |
---|
1578 | Sec.~\ref{sec:atmospherics} or Ref.~\cite{Huber:2005ep}). |
---|
1579 | |
---|
1580 | |
---|
1581 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1582 | \section{Synergies provided by the CERN--MEMPHYS facilities} |
---|
1583 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1584 | \label{sec:synergies} |
---|
1585 | |
---|
1586 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1587 | \subsection{Combining Beta Beam and Super Beam} |
---|
1588 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1589 | \label{sec:synergies-beams} |
---|
1590 | |
---|
1591 | In this section we discuss synergies which emerge if both \BB\ and SPL |
---|
1592 | are available. The main difference between these two beams is the |
---|
1593 | different initial neutrino flavor, |
---|
1594 | $\stackrel{\scriptscriptstyle(-)}{\nu}_e$ for \BB\ and |
---|
1595 | $\stackrel{\scriptscriptstyle (-)}{\nu}_\mu$ for SPL. This implies |
---|
1596 | that at near detectors all relevant cross sections can be measured. In |
---|
1597 | particular, the near detector of the \BB\ will measure the cross |
---|
1598 | section for the SPL appearance search, and vice versa. |
---|
1599 | % |
---|
1600 | If both experiments run with neutrinos and antineutrinos all possible |
---|
1601 | transition probabilities are covered: $P_{\nu_e\to\nu_\mu}$, |
---|
1602 | $P_{\bar\nu_e\to\bar\nu_\mu}$, $P_{\nu_\mu\to\nu_e}$, and |
---|
1603 | $P_{\bar\nu_\mu\to\bar\nu_e}$. Together with the fact that matter |
---|
1604 | effects are very small because of the relatively short baseline, this |
---|
1605 | means that in addition to CP also direct tests of the T and CPT |
---|
1606 | symmetries are possible. |
---|
1607 | |
---|
1608 | \begin{figure}[!t] |
---|
1609 | \centering |
---|
1610 | \includegraphics[width=0.9\textwidth]{./fig14.eps} |
---|
1611 | % |
---|
1612 | \mycaption{Discovery potential of a finite value of $\stheta$ at |
---|
1613 | $3\sigma$ $(\Delta\chi^2>9)$ for 5~yrs neutrino data from |
---|
1614 | \BB, SPL, and the combination of \BB\ + SPL compared to |
---|
1615 | 10~yrs data from T2HK (2~yrs neutrinos + 8~yrs antineutrinos). |
---|
1616 | \label{fig:th13-5yrs}} |
---|
1617 | \end{figure} |
---|
1618 | |
---|
1619 | However, if the CPT symmetry is assumed in principle all information |
---|
1620 | can be obtained just from neutrino data because of the relations |
---|
1621 | $P_{\bar\nu_e\to\bar\nu_\mu} = P_{\nu_\mu\to\nu_e}$ and |
---|
1622 | $P_{\bar\nu_\mu\to\bar\nu_e} = P_{\nu_e\to\nu_\mu}$. As mentioned |
---|
1623 | already in Sec.~\ref{sec:degeneracies} this implies that (time |
---|
1624 | consuming) antineutrino running can be avoided. We illustrate this |
---|
1625 | synergy in Figs.~\ref{fig:th13-5yrs} and \ref{fig:CP-5yrs}. In |
---|
1626 | Fig.~\ref{fig:th13-5yrs} we show the $\theta_{13}$ discovery potential |
---|
1627 | of 5 years of neutrino data from \BB\ and SPL. From the left panel the |
---|
1628 | complementarity of the two experiments is obvious, since each of them |
---|
1629 | is most sensitive in a different region of \delCP. (As expected from |
---|
1630 | general properties of the oscillation probabilities the sensitivity |
---|
1631 | curves of \BB\ and SPL are approximately related by the transformation |
---|
1632 | $\delCP \to 2\pi - \delCP$.) Combining these two data sets results in |
---|
1633 | a sensitivity slightly better than from 10 years (2$\nu$+8$\bar\nu$) |
---|
1634 | of T2HK data. |
---|
1635 | % |
---|
1636 | As visible in Fig.~\ref{fig:CP-5yrs} also for the CPV discovery this |
---|
1637 | synergy works and 5 years of neutrino data from \BB\ and SPL lead to a |
---|
1638 | similar sensitivity as 10 years of T2HK. |
---|
1639 | |
---|
1640 | \begin{figure}[!t] |
---|
1641 | \centering |
---|
1642 | \includegraphics[width=0.6\textwidth]{./fig15.eps} |
---|
1643 | % |
---|
1644 | \mycaption{Sensitivity to CPV at $3\sigma$ $(\Delta\chi^2>9)$ for |
---|
1645 | combining 5~yrs neutrino data from \BB\ and SPL compared to |
---|
1646 | 10~yrs data from T2HK (2~yrs neutrinos + 8~yrs antineutrinos). |
---|
1647 | \label{fig:CP-5yrs}} |
---|
1648 | \end{figure} |
---|
1649 | |
---|
1650 | |
---|
1651 | |
---|
1652 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1653 | \subsection{Resolving degeneracies with atmospheric neutrinos} |
---|
1654 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1655 | \label{sec:atmospherics} |
---|
1656 | |
---|
1657 | It was pointed out in Ref.~\cite{Huber:2005ep} that for LBL |
---|
1658 | experiments based on mega ton scale water \v{C}erenkov detectors data |
---|
1659 | from atmospheric neutrinos (ATM) provide an attractive method to |
---|
1660 | resolve degeneracies. Atmospheric neutrinos are sensitive to the |
---|
1661 | neutrino mass hierarchy if $\theta_{13}$ is sufficiently large due to |
---|
1662 | Earth matter effects, mainly in multi-GeV $e$-like |
---|
1663 | events~\cite{Petcov:1998su,Akhmedov:1998ui,Bernabeu:2003yp}. Moreover, |
---|
1664 | sub-GeV $e$-like events provide sensitivity to the octant of |
---|
1665 | $\theta_{23}$~\cite{Kim:1998bv,Peres:2003wd,Gonzalez-Garcia:2004cu} |
---|
1666 | due to oscillations with $\Delta m^2_{21}$ (see also |
---|
1667 | Ref.~\cite{Kajita} for a discussion of atmospheric neutrinos in the |
---|
1668 | context of Hyper-K). |
---|
1669 | % |
---|
1670 | Following Ref.~\cite{Huber:2005ep} we investigate here the synergy |
---|
1671 | from a combination of LBL data from \BB\ and SPL with ATM data in the |
---|
1672 | MEMPHYS detector. Technical details are given in |
---|
1673 | Sec.~\ref{sec:atm-details}. |
---|
1674 | |
---|
1675 | The effect of degeneracies in LBL data has been discussed in |
---|
1676 | Sec.~\ref{sec:degeneracies}, see Figs.~\ref{fig:degeneracies} and |
---|
1677 | \ref{fig:degeneracies_SPL}. As discussed there, for given true |
---|
1678 | parameter values the data can be fitted with the wrong hierarchy |
---|
1679 | and/or with the wrong octant of $\theta_{23}$. Hence, from LBL data |
---|
1680 | alone the hierarchy and the octant cannot be determined and |
---|
1681 | ambiguities exist in the determination of $\theta_{13}$ and |
---|
1682 | $\delta_\mathrm{CP}$. |
---|
1683 | % |
---|
1684 | If the LBL data are combined with ATM data only the colored regions in |
---|
1685 | Fig.~\ref{fig:degeneracies} survive, i.e., in this particular example |
---|
1686 | for SPL and T2HK the degeneracies are completely lifted at 95\%~CL, |
---|
1687 | the mass hierarchy and the octant of $\theta_{23}$ can be identified, |
---|
1688 | and the ambiguities in $\theta_{13}$ and $\delta_\mathrm{CP}$ are |
---|
1689 | resolved. For the \BB\ an island corresponding to the wrong hierarchy |
---|
1690 | does survive at the 95\%~CL for 2~dof. Still, the solution with the |
---|
1691 | wrong sign of $\Delta m^2_{31}$ is disfavored with $\Delta\chi^2 = |
---|
1692 | 5.1$ with respect to the true solution, which corresponds to |
---|
1693 | 2.4$\sigma$ for 1~dof. |
---|
1694 | % |
---|
1695 | Let us note that in Fig.~\ref{fig:degeneracies} we have chosen a |
---|
1696 | favorable value of $\sin^2\theta_{23} = 0.6$; for values |
---|
1697 | $\sin^2\theta_{23} < 0.5$ in general the sensitivity of ATM data is |
---|
1698 | weaker~\cite{Huber:2005ep}. |
---|
1699 | |
---|
1700 | \begin{figure}[!t] |
---|
1701 | \centering |
---|
1702 | \includegraphics[width=0.9\textwidth]{./fig16.eps} |
---|
1703 | % |
---|
1704 | \mycaption{Sensitivity to the mass hierarchy at $2\sigma$ |
---|
1705 | $(\Delta\chi^2 = 4)$ as a function of the true values of |
---|
1706 | $\sin^22\theta_{13}$ and $\delta_\mathrm{CP}$ (left), and the |
---|
1707 | fraction of true values of $\delCP$ (right). The solid curves are |
---|
1708 | the sensitivities from the combination of long-baseline and |
---|
1709 | atmospheric neutrino data, the dashed curves correspond to |
---|
1710 | long-baseline data only. The running time is ($5\nu + 5\bar\nu$)~yrs |
---|
1711 | for \BB\ and ($2\nu + 8\bar\nu$)~yrs for the Super Beams. For |
---|
1712 | comparison we show in the right panel also the sensitivities of |
---|
1713 | NO$\nu$A and NO$\nu$A+T2K extracted from Fig.~13.14 of |
---|
1714 | Ref.~\cite{Ayres:2004js}. For the curve labeled ``NO$\nu$A |
---|
1715 | (p.dr.)+T2K@4~MW'' a proton driver has been assumed for NO$\nu$A and |
---|
1716 | the T2K beam has been up-graded to 4~MW, see |
---|
1717 | Ref.~\cite{Ayres:2004js} for details.} |
---|
1718 | \label{fig:hierarchy} |
---|
1719 | \end{figure} |
---|
1720 | |
---|
1721 | In Fig.~\ref{fig:hierarchy} we show how the combination of ATM+LBL |
---|
1722 | data leads to a non-trivial sensitivity to the neutrino mass |
---|
1723 | hierarchy, i.e.\ to the sign of $\Delta m^2_{31}$. For LBL data alone |
---|
1724 | (dashed curves) there is practically no sensitivity for the |
---|
1725 | CERN--MEMPHYS experiments (because of the very small matter effects |
---|
1726 | due to the relatively short baseline), and the sensitivity of T2HK |
---|
1727 | depends strongly on the true value of $\delta_\mathrm{CP}$. However, |
---|
1728 | by including data from atmospheric neutrinos (solid curves) the mass |
---|
1729 | hierarchy can be identified at $2\sigma$~CL provided |
---|
1730 | $\sin^22\theta_{13} \gtrsim 0.02-0.03$. As an example we have chosen |
---|
1731 | in that figure a true value of $\theta_{23} = \pi/4$. Generically the |
---|
1732 | hierarchy sensitivity increases with increasing $\theta_{23}$, see |
---|
1733 | Ref.~\cite{Huber:2005ep} for a detailed discussion. |
---|
1734 | |
---|
1735 | The sensitivity to the neutrino mass hierarchy shown in |
---|
1736 | Fig.~\ref{fig:hierarchy} is significantly improved with respect to our |
---|
1737 | previous results obtained in Ref.~\cite{Huber:2005ep}. There are two |
---|
1738 | main reasons for this improved performance: First, we use now much |
---|
1739 | more bins in charged lepton energy for fully contained single-ring |
---|
1740 | events\footnote{The impact of energy binning on the hierarchy |
---|
1741 | determination with atmospheric neutrinos has been discussed recently |
---|
1742 | in Ref.~\cite{Petcov:2005rv} in the context of magnetized iron |
---|
1743 | detectors.} (compare Sec.~\ref{sec:atm-details}), and second, we |
---|
1744 | implemented also information from multi-ring events. This latter point |
---|
1745 | is important since the relative contribution of neutrinos and |
---|
1746 | antineutrinos is different for single- and multi-ring |
---|
1747 | events. Therefore, combining single- and multi-ring data allows to |
---|
1748 | obtain a discrimination between neutrino and antineutrino events on a |
---|
1749 | statistical basis. This in turn contains crucial information on the |
---|
1750 | hierarchy, since the matter enhancement is visible either in neutrinos |
---|
1751 | or antineutrinos, depending on the hierarchy. |
---|
1752 | |
---|
1753 | Although \BB\ and SPL alone have no sensitivity to the hierarchy at |
---|
1754 | all, we find that the combination of them does provide rather good |
---|
1755 | sensitivity even without atmospheric data. The reason for this |
---|
1756 | interesting effect is the following. Because of the rather short |
---|
1757 | baseline the matter effect is too small to distinguish between NH and |
---|
1758 | IH given only neutrino and antineutrino information in one channel. |
---|
1759 | However, the tiny matter effect suffices to move the hierarchy |
---|
1760 | degenerate solution to slightly different locations in the ($\stheta$, |
---|
1761 | $\delCP$) plane for the $\stackrel{\scriptscriptstyle(-)}{\nu}_e \to |
---|
1762 | \stackrel{\scriptscriptstyle (-)}{\nu}_\mu$ (\BB) and |
---|
1763 | $\stackrel{\scriptscriptstyle(-)}{\nu}_\mu \to |
---|
1764 | \stackrel{\scriptscriptstyle (-)}{\nu}_e$ (SPL) channels (compare |
---|
1765 | Fig.~\ref{fig:degeneracies}). Hence, if all four CP and T conjugate |
---|
1766 | channels are available (as it is the case for the \BB+SPL combination) |
---|
1767 | already the small matter effect picked up along the 130~km |
---|
1768 | CERN--MEMPHYS distance provides sensitivity to the mass hierarchy for |
---|
1769 | $\sin^22\theta_{13} \gtrsim 0.03$, or $\sin^22\theta_{13} \gtrsim 0.015$ |
---|
1770 | if also atmospheric neutrino data is included. |
---|
1771 | |
---|
1772 | For comparison we show in the right panel of Fig.~\ref{fig:hierarchy} |
---|
1773 | also the sensitivity of the NO$\nu$A~\cite{Ayres:2004js} experiment, |
---|
1774 | and of NO$\nu$A+T2K, where in the second case a beam upgrade by a |
---|
1775 | proton driver has been assumed for NO$\nu$A, and for T2K the |
---|
1776 | Super-Kamiokande detector has been used but the beam intensity has |
---|
1777 | been increased by assuming 4~MW power. More details on these |
---|
1778 | sensitivities can be found in Ref.~\cite{Ayres:2004js}. |
---|
1779 | % |
---|
1780 | Let us note that in general LBL experiments with two detectors and/or |
---|
1781 | very long baselines ($\gtrsim 1000$~km) are a competitive method to |
---|
1782 | atmospheric neutrinos for the hierarchy determination, see, e.g., |
---|
1783 | Refs.~\cite{Ishitsuka:2005qi,Kajita:2006bt,MenaRequejo:2005hn,Hagiwara:2005pe,Barger:2006vy} |
---|
1784 | for recent analyses. In particular, in case of the T2KK extension of |
---|
1785 | the T2HK experiment, the very long baseline to Korea allows for a |
---|
1786 | determination of the mass hierarchy down to $\sin^22\theta_{13} |
---|
1787 | \gtrsim 0.02$ ($2\sigma$) without using atmospheric |
---|
1788 | neutrinos~\cite{Kajita:2006bt}. |
---|
1789 | % |
---|
1790 | We mention also the possibility to determine the neutrino mass |
---|
1791 | hierarchy by using neutrino events from a galactic Super Nova |
---|
1792 | explosion in mega ton \v{C}erenkov detectors such as MEMPHYS, see, |
---|
1793 | e.g., Ref.~\cite{Kachelriess:2004vs}. |
---|
1794 | |
---|
1795 | \begin{figure}[!t] |
---|
1796 | \centering |
---|
1797 | \includegraphics[width=0.55\textwidth]{./fig17.eps} |
---|
1798 | % |
---|
1799 | \mycaption{$\Delta\chi^2$ of the solution with the wrong octant of |
---|
1800 | $\theta_{23}$ as a function of the true value of |
---|
1801 | $\sin^2\theta_{23}$. We have assumed a true value of $\theta_{13} = |
---|
1802 | 0$, and the running time is ($2\nu + 8\bar\nu$)~yrs.} |
---|
1803 | \label{fig:octant} |
---|
1804 | \end{figure} |
---|
1805 | |
---|
1806 | Fig.~\ref{fig:octant} shows the potential of ATM+LBL data to exclude |
---|
1807 | the octant degenerate solution. Since this effect is based mainly on |
---|
1808 | oscillations with $\Delta m^2_{21}$ there is very good sensitivity |
---|
1809 | even for $\theta_{13} = 0$; a finite value of $\theta_{13}$ in general |
---|
1810 | improves the sensitivity~\cite{Huber:2005ep}. From the figure one can |
---|
1811 | read off that atmospheric data alone can can resolve the correct |
---|
1812 | octant at $3\sigma$ if $|\sin^2\theta_{23} - 0.5| \gtrsim 0.085$. If |
---|
1813 | atmospheric data is combined with the LBL data from SPL or T2HK there |
---|
1814 | is sensitivity to the octant for $|\sin^2\theta_{23} - 0.5| \gtrsim |
---|
1815 | 0.05$. The improvement of the octant sensitivity with respect to |
---|
1816 | previous analyses~\cite{Huber:2005ep,Gonzalez-Garcia:2004cu} follows |
---|
1817 | from changes in the analysis of sub-GeV atmospheric events, where now |
---|
1818 | three bins in lepton momentum are used instead of one. Note that since |
---|
1819 | in Fig.~\ref{fig:octant} we have assumed a true value of $\theta_{13} |
---|
1820 | = 0$, combining the \BB\ with ATM does not improve the sensitivity |
---|
1821 | with respect to atmospheric data alone. |
---|
1822 | % |
---|
1823 | We note that the T2KK configuration provides also some sensitivity to |
---|
1824 | the octant of $\theta_{23}$ without referring to atmospheric |
---|
1825 | neutrinos. In Ref.~\cite{Kajita:2006bt} it was found that for |
---|
1826 | $|\sin^2\theta_{23} - 0.5| \gtrsim 0.12$ the octant can be identified |
---|
1827 | in T2KK at $3\sigma$. |
---|
1828 | |
---|
1829 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1830 | \section{Summary} |
---|
1831 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
1832 | \label{sec:conclusions} |
---|
1833 | |
---|
1834 | In this work we have studied the physics potential of the |
---|
1835 | CERN--MEMPHYS neutrino oscillation project. We consider a Beta Beam |
---|
1836 | (\BB) with $\gamma = 100$ for the stored ions, where existing |
---|
1837 | facilities at CERN can be used optimally, and a Super Beam based on an |
---|
1838 | optimized Super Proton Linac (SPL) with a beam energy of 3.5~GeV and |
---|
1839 | 4~MW power. As target we assume the MEMPHYS detector, a 440~kt water |
---|
1840 | \v{C}erenkov detector at Fr\'ejus, at a distance of 130~km from |
---|
1841 | CERN. The main characteristics of the experiments are summarized in |
---|
1842 | Tab.~\ref{tab:setups}. |
---|
1843 | % |
---|
1844 | The adopted neutrino fluxes are based on realistic calculations of ion |
---|
1845 | production and storage for the \BB, and a full simulation of the beam |
---|
1846 | line (particle production and decay of secondaries) for SPL. Special |
---|
1847 | care has be given to the issue of backgrounds, which we include by |
---|
1848 | means of detailed event simulations and applying Super-Kamiokande particle |
---|
1849 | identification algorithms. |
---|
1850 | |
---|
1851 | The physics potential of the \BB\ and SPL experiments in terms of |
---|
1852 | $\theta_{13}$ discovery reach and sensitivity to CP violation has been |
---|
1853 | addressed where parameter degeneracies are fully taken into account. |
---|
1854 | The main results on these performance indicators are summarized in |
---|
1855 | Figs.~\ref{fig:th13} and \ref{fig:CPV}. |
---|
1856 | % |
---|
1857 | We obtain a guaranteed discovery reach of $\stheta \simeq 5\times |
---|
1858 | 10^{-3}$ at $3\sigma$, irrespective of the actual value of \delCP. For |
---|
1859 | certain values of \delCP\ the sensitivity is significantly improved, |
---|
1860 | and for \BB\ (SPL) discovery limits around $\stheta \simeq 3\,(10) |
---|
1861 | \times 10^{-4}$ are possible for a large fraction of all possible |
---|
1862 | values of \delCP. |
---|
1863 | % |
---|
1864 | Maximal CP violation (for $\delCP^\mathrm{true} = \pi/2, \, 3\pi/2$) |
---|
1865 | can be discovered at $3\sigma$ down to $\stheta \simeq 2\, (9)\times |
---|
1866 | 10^{-4}$ for \BB\ (SPL), whereas the best sensitivity to CP violation |
---|
1867 | is obtained for $\stheta \sim 10^{-2}$: For $\stheta = 10^{-2}$ CP |
---|
1868 | violation can be established at $3\sigma$ for 78\% (73\%) of all |
---|
1869 | possible true values of \delCP\ for \BB\ (SPL). |
---|
1870 | % |
---|
1871 | We stress that the \BB\ performance in general depends crucially on |
---|
1872 | the number of ion decays per year. |
---|
1873 | % |
---|
1874 | The impact of the value of systematical uncertainties on signal and |
---|
1875 | background on our results is discussed. |
---|
1876 | % |
---|
1877 | The \BB\ and SPL sensitivities are compared to the ones of the |
---|
1878 | phase~II of the T2K experiment in Japan (T2HK), which is a competing |
---|
1879 | proposal of similar size and timescale. In general we obtain rather |
---|
1880 | similar sensitivities for T2HK and SPL, and hence the CERN--MEMPHYS |
---|
1881 | experiments provide a viable alternative to T2HK. We find that \BB\ |
---|
1882 | and SPL are less sensitive to systematical errors, whereas the |
---|
1883 | sensitivity of T2HK crucially depends on the systematical error on the |
---|
1884 | background.\footnote{Let us note that in the present study we have not |
---|
1885 | considered the recent ``T2KK'' proposal~\cite{Ishitsuka:2005qi}, where |
---|
1886 | one half of the Hyper-K detector mass is at Kamioka and the second |
---|
1887 | half in Korea. For such a setup our results do not apply and |
---|
1888 | especially the conclusion on systematical errors may be different.} |
---|
1889 | |
---|
1890 | Assuming that both \BB\ and SPL experiments are available, we point |
---|
1891 | out that one can benefit from the different oscillation channels |
---|
1892 | $\nu_e\to\nu_\mu$ for \BB\ and $\nu_\mu\to\nu_e$ for SPL, since by the |
---|
1893 | combination of these channels the time intensive antineutrino |
---|
1894 | measurements can be avoided. We show that 5 years of neutrino data from |
---|
1895 | \BB\ and SPL lead to similar results as 2 years of neutrino plus 8 |
---|
1896 | years of antineutrino data from T2HK. |
---|
1897 | % |
---|
1898 | Furthermore, we discuss the use of atmospheric neutrinos in the |
---|
1899 | MEMPHYS detector to resolve parameter degeneracies in the |
---|
1900 | long-baseline data. This effect leads to a sensitivity to the neutrino |
---|
1901 | mass hierarchy at $2\sigma$~CL for $\sin^22\theta_{13} \gtrsim |
---|
1902 | 0.025$ for \BB\ and SPL, although these experiments alone (without |
---|
1903 | atmospheric data) have no sensitivity at all. The optimal hierarchy |
---|
1904 | sensitivity is obtained from combining \BB+SPL+atmospheric data. |
---|
1905 | Furthermore, the combination of atmospheric data with a Super Beam |
---|
1906 | provides a possibility to determine the octant of $\theta_{23}$. |
---|
1907 | |
---|
1908 | To conclude, we have shown that the CERN--MEMPHYS neutrino oscillation |
---|
1909 | project based on a Beta Beam and/or a Super Beam plus a mega ton scale |
---|
1910 | water \v{C}erenkov detector offers interesting and competitive physics |
---|
1911 | possibilities and is worth to be considered as a serious option in |
---|
1912 | the worldwide process of identifying future high precision neutrino |
---|
1913 | oscillation facilities~\cite{ISSpage}. |
---|
1914 | |
---|
1915 | \subsection*{Acknowledgment} |
---|
1916 | |
---|
1917 | We thank J.~Argyriades for communication on the Super-K atmospheric |
---|
1918 | neutrino analysis, A.~Cazes for his work on the SPL simulation, and |
---|
1919 | P.~Huber for his patience in answering questions concerning the use of |
---|
1920 | GLoBES. Furthermore, we thank D.~Casper for the help in installing and |
---|
1921 | running Nuance, and E.~Couce for discussions about the \BB\ |
---|
1922 | backgrounds. T.S.\ is supported by the $6^\mathrm{th}$~Framework |
---|
1923 | Program of the European Community under a Marie Curie Intra-European |
---|
1924 | Fellowship. |
---|
1925 | |
---|
1926 | |
---|
1927 | %\newpage |
---|
1928 | \begin{thebibliography}{99} |
---|
1929 | |
---|
1930 | \bibitem{solar} |
---|
1931 | B.~T.~Cleveland {\it et al.}, |
---|
1932 | Astrophys.\ J.\ {\bf 496} (1998) 505; |
---|
1933 | %%CITATION = ASJOA,496,505;%% |
---|
1934 | % |
---|
1935 | J.N.~Abdurashitov {\it et al.} [SAGE], |
---|
1936 | J.\ Exp.\ Theor.\ Phys.\ {\bf 95} (2002) 181 |
---|
1937 | % [Zh.\ Eksp.\ Teor.\ Fiz.\ {\bf 122} (2002) 211]. |
---|
1938 | [astro-ph/0204245]; |
---|
1939 | %%CITATION = ASTRO-PH 0204245;%% |
---|
1940 | % |
---|
1941 | T. Kirsten {\it et al.} [GALLEX and GNO], |
---|
1942 | Nucl. Phys. B (Proc. Suppl.) {\bf 118} (2003) 33; |
---|
1943 | % |
---|
1944 | S.~Fukuda {\it et al.} [Super-Kamiokande], |
---|
1945 | %``Determination of solar neutrino |
---|
1946 | % oscillation parameters using 1496 days of Super-Kamiokande-I data,'' |
---|
1947 | Phys. Lett. {\bf B539} (2002) 179; |
---|
1948 | % |
---|
1949 | %\bibitem{ahmad:2002ka} |
---|
1950 | Q.R. Ahmad {\em et~al.} [SNO], |
---|
1951 | Phys. Rev. Lett. {\bf 89}, 011302 (2002) |
---|
1952 | [nucl-ex/0204009]; |
---|
1953 | %%CITATION = NUCL-EX 0204009;%% |
---|
1954 | % |
---|
1955 | %\bibitem{Aharmim:2005gt} |
---|
1956 | B.~Aharmim {\it et al.} [SNO], |
---|
1957 | %``Electron energy spectra, fluxes, and day-night asymmetries of B-8 solar |
---|
1958 | %neutrinos from the 391-day salt phase SNO data set,'' |
---|
1959 | Phys.\ Rev.\ C {\bf 72} (2005) 055502 |
---|
1960 | [nucl-ex/0502021]. |
---|
1961 | %%CITATION = NUCL-EX 0502021;%% |
---|
1962 | |
---|
1963 | \bibitem{Fukuda:1998mi} |
---|
1964 | Y.~Fukuda {\it et al.} [Super-Kamiokande Coll.], |
---|
1965 | %``Evidence for oscillation of atmospheric neutrinos,'' |
---|
1966 | Phys.\ Rev.\ Lett.\ {\bf 81} (1998) 1562 |
---|
1967 | [hep-ex/9807003]. |
---|
1968 | %%CITATION = HEP-EX 9807003;%% |
---|
1969 | |
---|
1970 | \bibitem{Ashie:2005ik} |
---|
1971 | Super-Kamiokande Coll., |
---|
1972 | Y.~Ashie {\it et al.}, %[Super-Kamiokande Collaboration], |
---|
1973 | %``A measurement of atmospheric neutrino oscillation parameters by |
---|
1974 | %Super-Kamiokande I,'' |
---|
1975 | Phys.\ Rev.\ D {\bf 71}, 112005 (2005) |
---|
1976 | [hep-ex/0501064]; |
---|
1977 | %%CITATION = HEP-EX 0501064;%% |
---|
1978 | % |
---|
1979 | %\bibitem{Hosaka:2006zd} |
---|
1980 | J.~Hosaka {\it et al.},% [Super-Kamiokande Collaboration], |
---|
1981 | %``Three flavor neutrino oscillation analysis of atmospheric neutrinos in |
---|
1982 | %Super-Kamiokande,'' |
---|
1983 | Phys.\ Rev.\ D {\bf 74}, 032002 (2006) |
---|
1984 | [hep-ex/0604011]. |
---|
1985 | %%CITATION = HEP-EX 0604011;%% |
---|
1986 | |
---|
1987 | |
---|
1988 | \bibitem{Araki:2004mb} |
---|
1989 | T.~Araki {\it et al.} [KamLAND Coll.], |
---|
1990 | %``Measurement of neutrino oscillation with KamLAND: Evidence of spectral |
---|
1991 | %distortion,'' |
---|
1992 | Phys.\ Rev.\ Lett.\ {\bf 94}, 081801 (2005) |
---|
1993 | [hep-ex/0406035]. |
---|
1994 | %%CITATION = HEP-EX 0406035;%% |
---|
1995 | |
---|
1996 | |
---|
1997 | \bibitem{Aliu:2004sq} |
---|
1998 | E.~Aliu {\it et al.} [K2K Coll.], |
---|
1999 | %``Evidence for muon neutrino oscillation in an accelerator-based |
---|
2000 | %experiment,'' |
---|
2001 | Phys.\ Rev.\ Lett.\ {\bf 94}, 081802 (2005) |
---|
2002 | [hep-ex/0411038]. |
---|
2003 | %%CITATION = HEP-EX 0411038;%% |
---|
2004 | |
---|
2005 | \bibitem{MINOS} |
---|
2006 | D.G.~Micheal {\it et al.} [MINOS Coll.], |
---|
2007 | %''Observation of muon neutrino disappearance with the {MINOS} detectors and |
---|
2008 | %the {NuMI} neutrino beam,'' |
---|
2009 | hep-ex/0607088. |
---|
2010 | |
---|
2011 | \bibitem{OPERA} |
---|
2012 | D. Autiero [OPERA Coll.], |
---|
2013 | Nucl.\ Phys.\ B (Proc. Suppl.) {\bf 143}, 257 (2005); |
---|
2014 | M. Guler \etal, \textit{Experiment proposal}, |
---|
2015 | CERN/SPSC 2000-028 SPSC/P318 LNGS P25/2000. |
---|
2016 | |
---|
2017 | \bibitem{CNGS} |
---|
2018 | G. Acquistapace \etal, CERN-98-02. |
---|
2019 | |
---|
2020 | \bibitem{LSND} |
---|
2021 | A. Athanassopoulos \etal, Phys.\ Rev.\ Lett.\ {\bf 81}, 1774 (1998); |
---|
2022 | A. Aguilar \etal, Phys.\ Rev.\ D {\bf 64}, 112007 (2001). |
---|
2023 | |
---|
2024 | \bibitem{MINIBOONE} |
---|
2025 | I. Stancu \etal, FERMILAB-TM-2207. |
---|
2026 | |
---|
2027 | \bibitem{FOGLILISI05} |
---|
2028 | G.~L.~Fogli, E.~Lisi, A.~Marrone and A.~Palazzo, |
---|
2029 | %``Global analysis of three-flavor neutrino masses and mixings,'' |
---|
2030 | Prog.\ Part.\ Nucl.\ Phys.\ {\bf 57}, 742 (2006) |
---|
2031 | [hep-ph/0506083]. |
---|
2032 | %%CITATION = HEP-PH 0506083;%% |
---|
2033 | |
---|
2034 | \bibitem{Maltoni:2004ei} |
---|
2035 | M.~Maltoni, T.~Schwetz, M.~A.~Tortola and J.~W.~F.~Valle, |
---|
2036 | %``Status of global fits to neutrino oscillations,'' |
---|
2037 | New J.\ Phys.\ {\bf 6}, 122 (2004) |
---|
2038 | [hep-ph/0405172]; |
---|
2039 | %%CITATION = HEP-PH 0405172;%% |
---|
2040 | % |
---|
2041 | %\bibitem{Schwetz:2005jr} |
---|
2042 | T.~Schwetz, |
---|
2043 | %``Neutrino oscillations: Current status and prospects,'' |
---|
2044 | Acta Phys.\ Polon.\ B {\bf 36}, 3203 (2005) |
---|
2045 | [hep-ph/0510331]. |
---|
2046 | %%CITATION = HEP-PH 0510331;%% |
---|
2047 | |
---|
2048 | \bibitem{PMNS} |
---|
2049 | B.~Pontecorvo, Sov.\ Phys.--JETP {\bf 6}, 429 (1957) |
---|
2050 | [Zh.\ Eksp.\ Teor.\ Fiz.\ \textbf{33}, 549 (1957)]; |
---|
2051 | Z.~Maki, M.~Nakagawa and S.~Sakata, |
---|
2052 | Prog.\ Theor.\ Phys.\ \textbf{28}, 870 (1962); |
---|
2053 | B.~Pontecorvo, Sov.\ Phys.--JETP \textbf{26}, 984 (1968) |
---|
2054 | [Zh. Eksp. Teor. Fiz. \textbf{53}, 1717 (1967)]; |
---|
2055 | V.~N.~Gribov and B.~Pontecorvo, |
---|
2056 | Phys.\ Lett.\ B \textbf{28}, 493 (1969). |
---|
2057 | |
---|
2058 | \bibitem{CHOOZ} |
---|
2059 | Chooz Collaboration, |
---|
2060 | M. Apollonio \etal, Phys.\ Lett.\ B {\bf 466}, 415 (1999); |
---|
2061 | %\bibitem{Apollonio:2002gd} |
---|
2062 | M.~Apollonio {\it et al.}, |
---|
2063 | %``Search for neutrino oscillations on a long base-line at the CHOOZ nuclear |
---|
2064 | %power station,'' |
---|
2065 | Eur.\ Phys.\ J.\ C {\bf 27}, 331 (2003) |
---|
2066 | [hep-ex/0301017]. |
---|
2067 | %%CITATION = HEP-EX 0301017;%% |
---|
2068 | |
---|
2069 | \bibitem{Wpaper} |
---|
2070 | K.~Anderson \etal, White paper report on using nuclear |
---|
2071 | reactors to search for a value of $\theta_{13}$, |
---|
2072 | hep-ex/0402041; |
---|
2073 | % |
---|
2074 | F.~Ardellier \etal, Letter of intent for Double-Chooz, |
---|
2075 | hep-ex/0405032. |
---|
2076 | |
---|
2077 | \bibitem{T2K} |
---|
2078 | Y.~Itow {\it et al.}, |
---|
2079 | The JHF-Kamioka neutrino project, |
---|
2080 | hep-ex/0106019; |
---|
2081 | %%CITATION = HEP-EX 0106019;%% |
---|
2082 | % |
---|
2083 | %\bibitem{Kobayashi:2005hu} |
---|
2084 | T.~Kobayashi, |
---|
2085 | %``Super beams,'' |
---|
2086 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 143} (2005) 303. |
---|
2087 | %%CITATION = NUPHZ,143,303;%% |
---|
2088 | |
---|
2089 | \bibitem{Ayres:2004js} |
---|
2090 | D.~S.~Ayres {\it et al.} [NOvA Coll.], |
---|
2091 | %``NOvA proposal to build a 30-kiloton off-axis detector to study neutrino |
---|
2092 | %oscillations in the Fermilab NuMI beamline,'' |
---|
2093 | hep-ex/0503053. |
---|
2094 | %%CITATION = HEP-EX 0503053;%% |
---|
2095 | |
---|
2096 | \bibitem{Huber:2003pm} |
---|
2097 | P.~Huber, M.~Lindner, T.~Schwetz and W.~Winter, |
---|
2098 | %``Reactor neutrino experiments compared to superbeams,'' |
---|
2099 | Nucl.\ Phys.\ B {\bf 665} (2003) 487 |
---|
2100 | [hep-ph/0303232]; |
---|
2101 | %%CITATION = HEP-PH 0303232;%% |
---|
2102 | % |
---|
2103 | %\bibitem{Huber:2004ug} |
---|
2104 | P.~Huber, M.~Lindner, M.~Rolinec, T.~Schwetz and W.~Winter, |
---|
2105 | %``Prospects of accelerator and reactor neutrino oscillation experiments for |
---|
2106 | %the coming ten years,'' |
---|
2107 | Phys.\ Rev.\ D {\bf 70} (2004) 073014 |
---|
2108 | [hep-ph/0403068]. |
---|
2109 | %%CITATION = HEP-PH 0403068;%% |
---|
2110 | |
---|
2111 | \bibitem{Albrow:2005kw} |
---|
2112 | M.~G.~Albrow {\it et al.}, |
---|
2113 | Physics at a Fermilab proton driver, |
---|
2114 | hep-ex/0509019. |
---|
2115 | %%CITATION = HEP-EX 0509019;%% |
---|
2116 | |
---|
2117 | \bibitem{SPL} |
---|
2118 | M.~Baylac {\it et al.}, |
---|
2119 | Conceptual design of the SPL II: A high-power superconducting H- linac |
---|
2120 | at CERN, CERN-2006-006. |
---|
2121 | |
---|
2122 | \bibitem{BNLHS} |
---|
2123 | %\bibitem{Diwan:2003bp} |
---|
2124 | M.~V.~Diwan {\it et al.}, |
---|
2125 | %``Very long baseline neutrino oscillation experiments for precise |
---|
2126 | %measurements of mixing parameters and CP violating effects,'' |
---|
2127 | Phys.\ Rev.\ D {\bf 68} (2003) 012002 |
---|
2128 | [hep-ph/0303081]. |
---|
2129 | %%CITATION = HEP-PH 0303081;%% |
---|
2130 | |
---|
2131 | \bibitem{zucchelli} |
---|
2132 | %\bibitem{Zucchelli:2002sa} |
---|
2133 | P.~Zucchelli, |
---|
2134 | %``A novel concept for a anti-nu/e / nu/e neutrino factory: The Beta Beam,'' |
---|
2135 | Phys.\ Lett.\ B {\bf 532} (2002) 166. |
---|
2136 | %%CITATION = PHLTA,B532,166;%% |
---|
2137 | |
---|
2138 | \bibitem{Albright:2004iw} |
---|
2139 | C.~Albright {\it et al.} [Neutrino Factory/Muon Collider Coll.], |
---|
2140 | %``The neutrino factory and Beta Beam experiments and development,'' |
---|
2141 | physics/0411123. |
---|
2142 | %%CITATION = PHYS-ICS 0411123;%% |
---|
2143 | |
---|
2144 | \bibitem{Blondel:2004ae} |
---|
2145 | A.~Blondel {\it et al.}, |
---|
2146 | ECFA/CERN studies of a European neutrino factory complex, |
---|
2147 | CERN-2004-002 |
---|
2148 | |
---|
2149 | \bibitem{Campagne:2004wt} |
---|
2150 | J.~E.~Campagne and A.~Cazes, |
---|
2151 | %``The theta(13) and delta(CP) sensitivities of the SPL-Frejus project |
---|
2152 | %revisited,'' |
---|
2153 | Eur.\ Phys.\ J.\ C {\bf 45} (2006) 643 |
---|
2154 | [hep-ex/0411062]. |
---|
2155 | %%CITATION = HEP-EX 0411062;%% |
---|
2156 | |
---|
2157 | \bibitem{Mezzetto:2003ub} |
---|
2158 | M.~Mezzetto, |
---|
2159 | %``Physics reach of the beta beam,'' |
---|
2160 | J.\ Phys.\ G {\bf 29} (2003) 1771 |
---|
2161 | [hep-ex/0302007]; |
---|
2162 | %%CITATION = HEP-EX 0302007;%% |
---|
2163 | % |
---|
2164 | J.~Bouchez, M.~Lindroos, M.~Mezzetto, |
---|
2165 | %``Beta Beams: Present design and expected performances,'' |
---|
2166 | AIP Conf.\ Proc.\ {\bf 721} (2004) 37 |
---|
2167 | [hep-ex/0310059]. |
---|
2168 | %%CITATION = HEP-EX 0310059;%% |
---|
2169 | |
---|
2170 | \bibitem{memphys} |
---|
2171 | A.~de Bellefon {\it et al.}, |
---|
2172 | MEMPHYS: A large scale water \v{C}erenkov detector |
---|
2173 | at Fr\'ejus, Contribution to the CERN strategic committee, |
---|
2174 | hep-ex/0607026,\\ |
---|
2175 | \verb!http://apc-p7.org/APC_CS/Experiences/MEMPHYS/! |
---|
2176 | |
---|
2177 | \bibitem{UNO} |
---|
2178 | C.~K.~Jung, |
---|
2179 | Feasibility of a next generation underground water Cherenkov detector: |
---|
2180 | UNO, hep-ex/0005046. |
---|
2181 | %%CITATION = HEP-EX 0005046;%% |
---|
2182 | |
---|
2183 | \bibitem{Nakamura:2003hk} |
---|
2184 | K.~Nakamura, |
---|
2185 | %``Hyper-Kamiokande: A next generation water Cherenkov detector,'' |
---|
2186 | Int.\ J.\ Mod.\ Phys.\ A {\bf 18} (2003) 4053. |
---|
2187 | %%CITATION = IMPAE,A18,4053;%% |
---|
2188 | |
---|
2189 | \bibitem{Huber:2005ep} |
---|
2190 | P.~Huber, M.~Maltoni, T.~Schwetz, |
---|
2191 | %``Resolving parameter degeneracies in long-baseline experiments by |
---|
2192 | %atmospheric neutrino data,'' |
---|
2193 | Phys.\ Rev.\ D {\bf 71} (2005) 053006 |
---|
2194 | [hep-ph/0501037]. |
---|
2195 | %%CITATION = HEP-PH 0501037;%% |
---|
2196 | |
---|
2197 | \bibitem{Globes} |
---|
2198 | P.~Huber, M.~Lindner and W.~Winter, |
---|
2199 | %``Simulation of long-baseline neutrino oscillation experiments with |
---|
2200 | %GLoBES,'' |
---|
2201 | Comput.\ Phys.\ Commun.\ {\bf 167} (2005) 195 |
---|
2202 | [hep-ph/0407333], |
---|
2203 | \verb!http://www.mpi-hd.mpg.de/lin/globes/! |
---|
2204 | |
---|
2205 | \bibitem{Huber:2002mx} |
---|
2206 | P.~Huber, M.~Lindner and W.~Winter, |
---|
2207 | %``Superbeams versus neutrino factories,'' |
---|
2208 | Nucl.\ Phys.\ B {\bf 645} (2002) 3 |
---|
2209 | [hep-ph/0204352]. |
---|
2210 | %%CITATION = HEP-PH 0204352;%% |
---|
2211 | |
---|
2212 | \bibitem{Nuance} |
---|
2213 | NUANCE event generator (v3), |
---|
2214 | \verb!http://nuint.ps.uci.edu/nuance/!, |
---|
2215 | D.~Casper, |
---|
2216 | %``The nuance neutrino physics simulation, and the future,'' |
---|
2217 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 112} (2002) 161 |
---|
2218 | [hep-ph/0208030]. |
---|
2219 | |
---|
2220 | |
---|
2221 | % T2KK %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
2222 | |
---|
2223 | \bibitem{Ishitsuka:2005qi} |
---|
2224 | M.~Ishitsuka, T.~Kajita, H.~Minakata and H.~Nunokawa, |
---|
2225 | %``Resolving neutrino mass hierarchy and CP degeneracy by two identical |
---|
2226 | %detectors with different baselines,'' |
---|
2227 | Phys.\ Rev.\ D {\bf 72} (2005) 033003 |
---|
2228 | [hep-ph/0504026]. |
---|
2229 | %%CITATION = HEP-PH 0504026;%% |
---|
2230 | |
---|
2231 | \bibitem{Kajita:2006bt} |
---|
2232 | T.~Kajita, H.~Minakata, S.~Nakayama and H.~Nunokawa, |
---|
2233 | %``Resolving eight-fold neutrino parameter degeneracy by two identical |
---|
2234 | %detectors with different baselines,'' |
---|
2235 | Phys.\ Rev.\ D {\bf 75}, 013006 (2007) |
---|
2236 | [hep-ph/0609286]. |
---|
2237 | %%CITATION = PHRVA,D75,013006;%% |
---|
2238 | |
---|
2239 | \bibitem{Hagiwara:2005pe} |
---|
2240 | K.~Hagiwara, N.~Okamura and K.~Senda, |
---|
2241 | %``Solving the neutrino parameter degeneracy by measuring the T2K off-axis |
---|
2242 | %beam in Korea,'' |
---|
2243 | Phys.\ Lett.\ B {\bf 637}, 266 (2006) |
---|
2244 | [hep-ph/0504061]. |
---|
2245 | %%CITATION = HEP-PH 0504061;%% |
---|
2246 | |
---|
2247 | |
---|
2248 | % BB %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
2249 | |
---|
2250 | \bibitem{MyNufact04} |
---|
2251 | M.~Mezzetto, |
---|
2252 | %``SPL and Beta Beams to the Frejus,'' |
---|
2253 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 149} (2005) 179. |
---|
2254 | |
---|
2255 | \bibitem{Donini:2004hu} |
---|
2256 | A.~Donini, E.~Fernandez-Martinez, P.~Migliozzi, S.~Rigolin and L.~Scotto Lavina, |
---|
2257 | %``Study of the eightfold degeneracy with a standard beta-beam and a |
---|
2258 | %super-beam facility,'' |
---|
2259 | Nucl.\ Phys.\ B {\bf 710}, 402 (2005) |
---|
2260 | [hep-ph/0406132]. |
---|
2261 | %%CITATION = HEP-PH 0406132;%% |
---|
2262 | |
---|
2263 | \bibitem{JJHigh2} |
---|
2264 | %\bibitem{Burguet-Castell:2005pa} |
---|
2265 | J.~Burguet-Castell, D.~Casper, E.~Couce, J.~J.~Gomez-Cadenas and P.~Hernandez, |
---|
2266 | %``Optimal beta-beam at the CERN-SPS,'' |
---|
2267 | Nucl.\ Phys.\ B {\bf 725} (2005) 306 |
---|
2268 | [hep-ph/0503021]. |
---|
2269 | %%CITATION = HEP-PH 0503021;%% |
---|
2270 | |
---|
2271 | \bibitem{LindnerBB} |
---|
2272 | %\bibitem{Huber:2005jk} |
---|
2273 | P.~Huber, M.~Lindner, M.~Rolinec and W.~Winter, |
---|
2274 | %``Physics and optimization of beta-beams: From low to very high gamma,'' |
---|
2275 | Phys.\ Rev.\ D {\bf 73}, 053002 (2006) |
---|
2276 | [hep-ph/0506237]. |
---|
2277 | %%CITATION = HEP-PH 0506237;%% |
---|
2278 | |
---|
2279 | \bibitem{JJHigh1} |
---|
2280 | J.~Burguet-Castell, D.~Casper, J.~J.~Gomez-Cadenas, P.~Hernandez and F.~Sanchez, |
---|
2281 | Nucl.\ Phys.\ B {\bf 695} (2004) 217 |
---|
2282 | [hep-ph/0312068]. |
---|
2283 | |
---|
2284 | \bibitem{Terranova} |
---|
2285 | F.~Terranova, A.~Marotta, P.~Migliozzi and M.~Spinetti, |
---|
2286 | %``High energy beta beams without massive detectors,'' |
---|
2287 | Eur.\ Phys.\ J.\ C {\bf 38}, 69 (2004) |
---|
2288 | [hep-ph/0405081]. |
---|
2289 | %%CITATION = HEP-PH 0405081;%% |
---|
2290 | |
---|
2291 | \bibitem{BB-Reviews} |
---|
2292 | M.~Mezzetto, %``Beta Beams,'' |
---|
2293 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 143} (2005) 309 |
---|
2294 | [hep-ex/0410083]; |
---|
2295 | % |
---|
2296 | C.~Volpe, |
---|
2297 | %``Topical review on 'beta-beams','' |
---|
2298 | hep-ph/0605033. |
---|
2299 | |
---|
2300 | \bibitem{Volpe} |
---|
2301 | C.~Volpe, |
---|
2302 | %``What about a Beta Beam facility for low energy neutrinos?,'' |
---|
2303 | J.\ Phys.\ G {\bf 30} (2004) L1 |
---|
2304 | [hep-ph/0303222]. |
---|
2305 | |
---|
2306 | \bibitem{Lindroos} |
---|
2307 | %\bibitem{Autin:2002ms} |
---|
2308 | B.~Autin {\it et al.}, |
---|
2309 | %``The acceleration and storage of radioactive ions for a neutrino factory,'' |
---|
2310 | J.\ Phys.\ G {\bf 29}, 1785 (2003) |
---|
2311 | [physics/0306106]; |
---|
2312 | %%CITATION = PHYS-ICS 0306106;%% |
---|
2313 | % |
---|
2314 | M.~Benedikt, S.~Hancock and M.~Lindroos, |
---|
2315 | % ``Baseline Design for a Beta-Beam Neutrino Factory'', |
---|
2316 | Proceedings of EPAC, 2004, |
---|
2317 | \verb!http://accelconf.web.cern.ch/AccelConf/e04!; |
---|
2318 | % |
---|
2319 | M.~Lindroos, EURISOL DS/TASK12/TN-05-02. |
---|
2320 | |
---|
2321 | \bibitem{Eurisol} |
---|
2322 | Eurisol Beta Beam webpage: \verb!http://beta-beam.web.cern.ch/beta-beam/!. |
---|
2323 | |
---|
2324 | \bibitem{Lindroos-Optimization} |
---|
2325 | M.~Benedikt, A.~Fabich, S.~Hancock and M.~Lindroos, |
---|
2326 | %``Optimization Of The Beta-Beam Baseline,'' |
---|
2327 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 155} (2006) 211. |
---|
2328 | |
---|
2329 | \bibitem{MezzettoNuFact05} |
---|
2330 | M.~Mezzetto, |
---|
2331 | %``Physics potential of the gamma = 100,100 beta beam,'' |
---|
2332 | Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 155} (2006) 214 |
---|
2333 | [hep-ex/0511005]. |
---|
2334 | |
---|
2335 | % SPL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
2336 | |
---|
2337 | \bibitem{Neugen} |
---|
2338 | The NEUGEN neutrino event generator, |
---|
2339 | \verb!http://minos.phy.tufts.edu/gallag/neugen/!. |
---|
2340 | |
---|
2341 | \bibitem{FLUKA} |
---|
2342 | A.~Fasso \etal, Proceedings of the MonteCarlo 2000 conference, |
---|
2343 | Lisbon, October 26 2000, |
---|
2344 | A.~Kling \etal\ (eds.), Springer-Verlag Berlin (2001), 159-164 and 955-960. |
---|
2345 | |
---|
2346 | \bibitem{GEANT} |
---|
2347 | Application Software group, Computing and Network Division \etal, |
---|
2348 | GEANT Description and Simulation Tool, CERN Geneva, Switzerland |
---|
2349 | |
---|
2350 | \bibitem{HARP-MINERVA} |
---|
2351 | C. Catanesi \etal\ [HARP Coll.], CERN-SPSC 2002/019; |
---|
2352 | % |
---|
2353 | %\bibitem{Drakoulakos:2004gn} |
---|
2354 | D.~Drakoulakos {\it et al.} [Minerva Coll.], |
---|
2355 | %``Proposal to perform a high-statistics neutrino scattering experiment using |
---|
2356 | %a fine-grained detector in the NuMI beam,'' |
---|
2357 | hep-ex/0405002. |
---|
2358 | %%CITATION = HEP-EX 0405002;%% |
---|
2359 | |
---|
2360 | \bibitem{Mezzetto:2003mm} |
---|
2361 | M.~Mezzetto, |
---|
2362 | %``Physics potential of the SPL super beam,'' |
---|
2363 | J.\ Phys.\ G {\bf 29}, 1781 (2003) |
---|
2364 | [hep-ex/0302005]. |
---|
2365 | %%CITATION = HEP-EX 0302005;%% |
---|
2366 | |
---|
2367 | % ATM %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
2368 | |
---|
2369 | \bibitem{Honda:2004yz} |
---|
2370 | M.~Honda, T.~Kajita, K.~Kasahara and S.~Midorikawa, |
---|
2371 | %``A new calculation of the atmospheric neutrino flux in a 3-dimensional |
---|
2372 | %scheme,'' |
---|
2373 | Phys.\ Rev.\ D {\bf 70} (2004) 043008 |
---|
2374 | [astro-ph/0404457]. |
---|
2375 | %%CITATION = ASTRO-PH 0404457;%% |
---|
2376 | |
---|
2377 | \bibitem{Lipari:1991ut} |
---|
2378 | P.~Lipari and T.~Stanev, |
---|
2379 | %``Propagation of multi - TeV muons,'' |
---|
2380 | Phys.\ Rev.\ D {\bf 44} (1991) 3543. |
---|
2381 | %%CITATION = PHRVA,D44,3543;%% |
---|
2382 | |
---|
2383 | \bibitem{Gonzalez-Garcia:2004wg} |
---|
2384 | M.~C.~Gonzalez-Garcia and M.~Maltoni, |
---|
2385 | %``Atmospheric neutrino oscillations and new physics,'' |
---|
2386 | Phys.\ Rev.\ D {\bf 70} (2004) 033010 |
---|
2387 | [hep-ph/0404085]. |
---|
2388 | %%CITATION = HEP-PH 0404085;%% |
---|
2389 | |
---|
2390 | % DEGENERACIES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
2391 | |
---|
2392 | \bibitem{Burguet-Castell:2001ez} |
---|
2393 | J.~Burguet-Castell, M.~B.~Gavela, J.~J.~Gomez-Cadenas, P.~Hernandez and O.~Mena, |
---|
2394 | %``On the measurement of leptonic CP violation,'' |
---|
2395 | Nucl.\ Phys.\ B {\bf 608} (2001) 301 |
---|
2396 | [hep-ph/0103258]. |
---|
2397 | %%CITATION = HEP-PH 0103258;%% |
---|
2398 | |
---|
2399 | \bibitem{Minakata:2001qm} |
---|
2400 | H.~Minakata and H.~Nunokawa, |
---|
2401 | %``Exploring neutrino mixing with low energy superbeams,'' |
---|
2402 | JHEP {\bf 0110}, 001 (2001) |
---|
2403 | [hep-ph/0108085]. |
---|
2404 | %%CITATION = HEP-PH 0108085;%% |
---|
2405 | |
---|
2406 | \bibitem{Fogli:1996pv} |
---|
2407 | G.~L.~Fogli and E.~Lisi, |
---|
2408 | %``Tests of three-flavor mixing in long-baseline neutrino oscillation |
---|
2409 | %experiments,'' |
---|
2410 | Phys.\ Rev.\ D {\bf 54}, 3667 (1996) |
---|
2411 | [hep-ph/9604415]. |
---|
2412 | %%CITATION = HEP-PH 9604415;%% |
---|
2413 | |
---|
2414 | \bibitem{Barger:2001yr} |
---|
2415 | V.~Barger, D.~Marfatia and K.~Whisnant, |
---|
2416 | %``Breaking eight-fold degeneracies in neutrino CP violation, mixing, and |
---|
2417 | %mass hierarchy,'' |
---|
2418 | Phys.\ Rev.\ D {\bf 65}, 073023 (2002) |
---|
2419 | [hep-ph/0112119]. |
---|
2420 | %%CITATION = HEP-PH 0112119;%% |
---|
2421 | |
---|
2422 | \bibitem{Yasuda:2004gu} |
---|
2423 | O.~Yasuda, |
---|
2424 | %``New plots and parameter degeneracies in neutrino oscillations,'' |
---|
2425 | New J.\ Phys.\ {\bf 6}, 83 (2004) |
---|
2426 | [hep-ph/0405005]. |
---|
2427 | %%CITATION = HEP-PH 0405005;%% |
---|
2428 | |
---|
2429 | |
---|
2430 | \bibitem{Antusch:2004yx} |
---|
2431 | S.~Antusch, P.~Huber, J.~Kersten, T.~Schwetz and W.~Winter, |
---|
2432 | %``Is there maximal mixing in the lepton sector?,'' |
---|
2433 | Phys.\ Rev.\ D {\bf 70}, 097302 (2004) |
---|
2434 | [hep-ph/0404268]. |
---|
2435 | %%CITATION = HEP-PH 0404268;%% |
---|
2436 | |
---|
2437 | \bibitem{Minakata:2004pg} |
---|
2438 | H.~Minakata, M.~Sonoyama and H.~Sugiyama, |
---|
2439 | %``Determination of theta(23) in long-baseline neutrino oscillation |
---|
2440 | %experiments with three-flavor mixing effects,'' |
---|
2441 | Phys.\ Rev.\ D {\bf 70} (2004) 113012 |
---|
2442 | [hep-ph/0406073]. |
---|
2443 | %%CITATION = HEP-PH 0406073;%% |
---|
2444 | |
---|
2445 | \bibitem{Donini:2005db} |
---|
2446 | A.~Donini, E.~Fernandez-Martinez, D.~Meloni and S.~Rigolin, |
---|
2447 | %``nu/mu disappearance at the SPL, T2K-I, NOnuA and the neutrino factory,'' |
---|
2448 | Nucl.\ Phys.\ B {\bf 743}, 41 (2006) |
---|
2449 | [hep-ph/0512038]. |
---|
2450 | %%CITATION = HEP-PH 0512038;%% |
---|
2451 | |
---|
2452 | \bibitem{Peres:2003wd} |
---|
2453 | O.L.G.~Peres, A.Y.~Smirnov, |
---|
2454 | %``Atmospheric neutrinos: LMA oscillations, U(e3) induced interference and |
---|
2455 | %CP-violation,'' |
---|
2456 | Nucl.\ Phys.\ B {\bf 680} (2004) 479 |
---|
2457 | [hep-ph/0309312]. |
---|
2458 | %%CITATION = HEP-PH 0309312;%% |
---|
2459 | |
---|
2460 | \bibitem{Gonzalez-Garcia:2004cu} |
---|
2461 | M.C.~Gonzalez-Garcia, M.~Maltoni, A.Y. Smirnov, |
---|
2462 | %``Measuring the deviation of the 2-3 lepton mixing from maximal with |
---|
2463 | %atmospheric neutrinos,'' |
---|
2464 | Phys.\ Rev.\ D {\bf 70} (2004) 093005 |
---|
2465 | [hep-ph/0408170]. |
---|
2466 | %%CITATION = HEP-PH 0408170;%% |
---|
2467 | |
---|
2468 | \bibitem{Petcov:1998su} |
---|
2469 | S.~T.~Petcov, |
---|
2470 | %``Diffractive-like (or parametric-resonance-like?) enhancement of the earth |
---|
2471 | %(day-night) effect for solar neutrinos crossing the earth core,'' |
---|
2472 | Phys.\ Lett.\ B {\bf 434} (1998) 321 |
---|
2473 | [hep-ph/9805262]; |
---|
2474 | %%CITATION = HEP-PH 9805262;%% |
---|
2475 | % |
---|
2476 | %\bibitem{Chizhov:1998ug} |
---|
2477 | M.~Chizhov, M.~Maris and S.~T.~Petcov, |
---|
2478 | %``On the oscillation length resonance in the transitions of solar and |
---|
2479 | %atmospheric neutrinos crossing the earth core,'' |
---|
2480 | hep-ph/9810501; |
---|
2481 | %%CITATION = HEP-PH 9810501;%% |
---|
2482 | % |
---|
2483 | %\bibitem{Chizhov:1999az} |
---|
2484 | M.~V.~Chizhov and S.~T.~Petcov, |
---|
2485 | %``New conditions for a total neutrino conversion in a medium,'' |
---|
2486 | Phys.\ Rev.\ Lett.\ {\bf 83} (1999) 1096 |
---|
2487 | [hep-ph/9903399]. |
---|
2488 | %%CITATION = HEP-PH 9903399;%% |
---|
2489 | |
---|
2490 | \bibitem{Akhmedov:1998ui} |
---|
2491 | E.~K.~Akhmedov, |
---|
2492 | %``Parametric resonance of neutrino oscillations and passage of solar and |
---|
2493 | %atmospheric neutrinos through the earth,'' |
---|
2494 | Nucl.\ Phys.\ B {\bf 538}, 25 (1999) |
---|
2495 | [hep-ph/9805272]; |
---|
2496 | %%CITATION = HEP-PH 9805272;%% |
---|
2497 | % |
---|
2498 | %\bibitem{Akhmedov:1998xq} |
---|
2499 | E.~K.~Akhmedov, A.~Dighe, P.~Lipari and A.~Y.~Smirnov, |
---|
2500 | %``Atmospheric neutrinos at Super-Kamiokande and parametric resonance in |
---|
2501 | %neutrino oscillations,'' |
---|
2502 | Nucl.\ Phys.\ B {\bf 542}, 3 (1999) |
---|
2503 | [hep-ph/9808270]. |
---|
2504 | %%CITATION = HEP-PH 9808270;%% |
---|
2505 | |
---|
2506 | \bibitem{Bernabeu:2003yp} |
---|
2507 | J.~Bernabeu, S.~Palomares-Ruiz and S.~T.~Petcov, |
---|
2508 | %``Atmospheric neutrino oscillations, theta(13) and neutrino mass |
---|
2509 | %hierarchy,'' |
---|
2510 | Nucl.\ Phys.\ B {\bf 669}, 255 (2003) |
---|
2511 | [hep-ph/0305152]. |
---|
2512 | %%CITATION = HEP-PH 0305152;%% |
---|
2513 | |
---|
2514 | \bibitem{Kim:1998bv} |
---|
2515 | C.~W.~Kim and U.~W.~Lee, |
---|
2516 | %``Comment on the possible electron-neutrino excess in the Super-Kamiokande |
---|
2517 | %atmospheric neutrino experiment,'' |
---|
2518 | Phys.\ Lett.\ B {\bf 444}, 204 (1998) |
---|
2519 | [hep-ph/9809491]. |
---|
2520 | %%CITATION = HEP-PH 9809491;%% |
---|
2521 | |
---|
2522 | \bibitem{Kajita} |
---|
2523 | T.~Kajita, Talk at NNN05, 7--9 April 2005, Aussois, Savoie, France,\\ |
---|
2524 | \verb!http://nnn05.in2p3.fr/! |
---|
2525 | |
---|
2526 | \bibitem{Petcov:2005rv} |
---|
2527 | S.~T.~Petcov and T.~Schwetz, |
---|
2528 | %``Determining the neutrino mass hierarchy with atmospheric neutrinos,'' |
---|
2529 | Nucl.\ Phys.\ B {\bf 740}, 1 (2006) |
---|
2530 | [hep-ph/0511277]. |
---|
2531 | %%CITATION = HEP-PH 0511277;%% |
---|
2532 | |
---|
2533 | \bibitem{MenaRequejo:2005hn} |
---|
2534 | O.~Mena-Requejo, S.~Palomares-Ruiz and S.~Pascoli, |
---|
2535 | %``Super-NOvA: A long-baseline neutrino experiment with two off-axis |
---|
2536 | %detectors,'' |
---|
2537 | Phys.\ Rev.\ D {\bf 72} (2005) 053002 |
---|
2538 | [hep-ph/0504015]; |
---|
2539 | %%CITATION = HEP-PH 0504015;%% |
---|
2540 | % |
---|
2541 | %\bibitem{Mena:2005ri} |
---|
2542 | %O.~Mena, S.~Palomares-Ruiz and S.~Pascoli, |
---|
2543 | %``Determining the neutrino mass hierarchy and CP violation in NOnuA with a |
---|
2544 | %second off-axis detector,'' |
---|
2545 | Phys.\ Rev.\ D {\bf 73} (2006) 073007 |
---|
2546 | [hep-ph/0510182]. |
---|
2547 | %%CITATION = HEP-PH 0510182;%% |
---|
2548 | |
---|
2549 | \bibitem{Barger:2006vy} |
---|
2550 | V.~Barger {\it et al.}, |
---|
2551 | % M.~Dierckxsens, M.~Diwan, P.~Huber, C.~Lewis, D.~Marfatia and B.~Viren, |
---|
2552 | %``Precision physics with a wide band super neutrino beam,'' |
---|
2553 | Phys.\ Rev.\ D {\bf 74} (2006) 073004 |
---|
2554 | [hep-ph/0607177]. |
---|
2555 | %%CITATION = PHRVA,D74,073004;%% |
---|
2556 | |
---|
2557 | \bibitem{Kachelriess:2004vs} |
---|
2558 | M.~Kachelriess and R.~Tomas, |
---|
2559 | %``Identifying the neutrino mass hierarchy with supernova neutrinos,'' |
---|
2560 | hep-ph/0412100. |
---|
2561 | %%CITATION = HEP-PH 0412100;%% |
---|
2562 | |
---|
2563 | \bibitem{ISSpage} |
---|
2564 | Webpage of the International Scoping Study physics working group:\\ |
---|
2565 | \verb!http://www.hep.ph.ic.ac.uk/iss/wg1-phys-phen/index.html! |
---|
2566 | |
---|
2567 | \end{thebibliography} |
---|
2568 | \end{document} |
---|
2569 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
---|
2570 | |
---|
2571 | |
---|