1 | \relax |
---|
2 | \citation{SKNU04,K2KNU04} |
---|
3 | \citation{K2KNU04} |
---|
4 | \citation{MINOS} |
---|
5 | \citation{OPERA,ICARUS} |
---|
6 | \citation{CNGS} |
---|
7 | \citation{LSND} |
---|
8 | \citation{MINIBOONE} |
---|
9 | \citation{PMNS} |
---|
10 | \citation{CHOOZ} |
---|
11 | \citation{Wpaper} |
---|
12 | \citation{BETABEAM} |
---|
13 | \citation{NOVA,T2K} |
---|
14 | \citation{T2K,BNLHS,CERN} |
---|
15 | \citation{CERN} |
---|
16 | \citation{DONINI} |
---|
17 | \citation{DONINI,DOUBLE-CHOOZ} |
---|
18 | \citation{SPL} |
---|
19 | \citation{UNO} |
---|
20 | \citation{mosca} |
---|
21 | \citation{CERN} |
---|
22 | \citation{Meer} |
---|
23 | \citation{nuFact134,MMWPSCazes} |
---|
24 | \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}} |
---|
25 | \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Sketch of the SPL neutrino Superbeam from CERN to the Fr\'ejus tunnel.}}{2}} |
---|
26 | \newlabel{fig:Sbeam}{{1}{2}} |
---|
27 | \citation{DONINI,JJG,Mezzetto} |
---|
28 | \citation{nuFact138} |
---|
29 | \citation{fluka} |
---|
30 | \citation{CERN} |
---|
31 | \citation{SPL} |
---|
32 | \citation{MMWPSGaroby} |
---|
33 | \citation{nuFact134} |
---|
34 | \citation{harp} |
---|
35 | \citation{minerva} |
---|
36 | \citation{MARS} |
---|
37 | \citation{nuFact134} |
---|
38 | \citation{MMWPSGaroby} |
---|
39 | \@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Liquid mercury jet parameters.}}{3}} |
---|
40 | \newlabel{tab:targ}{{1}{3}} |
---|
41 | \@writefile{toc}{\contentsline {section}{\numberline {2}Target simulation}{3}} |
---|
42 | \newlabel{sec:target}{{2}{3}} |
---|
43 | \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Pion momentum distribution at the exit the target (a) and at the exit of the horns (b), simulated by FLUKA (\mbox {- - - -}) and by MARS (\mbox {------}).}}{3}} |
---|
44 | \newlabel{fig:compFlukaMars}{{2}{3}} |
---|
45 | \@writefile{toc}{\contentsline {section}{\numberline {3}Kaon production}{3}} |
---|
46 | \newlabel{sec:kaon}{{3}{3}} |
---|
47 | \citation{FLUKAprivate} |
---|
48 | \citation{geant} |
---|
49 | \citation{SIMONE1} |
---|
50 | \citation{nuFact138} |
---|
51 | \@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Average number of the most relevant secondary particles exiting the $30$\nobreakspace {}cm long, $1.5$\nobreakspace {}cm diameter mercury target per incident proton (FLUKA). The $\mu ^+/\mu ^-$ numbers and the $K^+/K^0$ numbers have been multiplied by $10^4$. Note that the $K^-$ production rate is at the level of $10^{-5}$ per incident proton.}}{4}} |
---|
52 | \newlabel{tab:nbPart}{{2}{4}} |
---|
53 | \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Kaon production (a) as a function of the incident proton beam energy ($E_p$) for $500\nobreakspace {}000$ incident protons with (\mbox {------}) curve for $K^+$, (\mbox {- - - -}) curve for $K^-$ and (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve for $K^o$. Pion production (b) in the same conditions with (\mbox {------}) curve for $\pi ^+$ and (\mbox {- - - -}) curve for $\pi ^-$.}}{4}} |
---|
54 | \newlabel{fig:KaonsPions}{{3}{4}} |
---|
55 | \@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Relevant parameters of horns. The shapes of the conductors are not changed by proton beam energy changes, as the focusing has been optimized for a defined pion momentum.}}{4}} |
---|
56 | \newlabel{tab:specif}{{3}{4}} |
---|
57 | \@writefile{toc}{\contentsline {section}{\numberline {4}Horn simulation}{4}} |
---|
58 | \newlabel{sec:horn}{{4}{4}} |
---|
59 | \citation{donega} |
---|
60 | \citation{donega} |
---|
61 | \citation{donega} |
---|
62 | \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Design of the Horn and the Reflector conductor shapes implemented in the GEANT simulation. The Hg target is located inside the cylindrical part of the Horn.}}{5}} |
---|
63 | \newlabel{fig:plan}{{4}{5}} |
---|
64 | \@writefile{toc}{\contentsline {section}{\numberline {5}Particle decay treatment and flux calculation}{5}} |
---|
65 | \@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Number of protons on target for different beam energy at 4\nobreakspace {}MW constant power.}}{5}} |
---|
66 | \newlabel{tab:proton}{{4}{5}} |
---|
67 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Algorithm description}{5}} |
---|
68 | \newlabel{sec:algo}{{5.1}{5}} |
---|
69 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Validation of the algorithm}{5}} |
---|
70 | \citation{donega} |
---|
71 | \citation{MEZZETTONUFACT060} |
---|
72 | \citation{DONINI-2} |
---|
73 | \citation{NUANCE} |
---|
74 | \citation{MEZZETTONUFACT060} |
---|
75 | \citation{UNO} |
---|
76 | \citation{mosca} |
---|
77 | \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Comparison between the probability method, (\mbox {------}) curve, and the full GEANT simulation method, (\mbox {- - - -}) curve, for the $\nu _\mu $ from $\pi ^+$ flux (left) and the $\mathaccent "7016\relax {\nu }_\mu $ from $\pi ^-$ flux (right). The horns are set to focus positive particles.}}{6}} |
---|
78 | \newlabel{fig:compGeantDonega}{{5}{6}} |
---|
79 | \@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Simulated fluxes}{6}} |
---|
80 | \@writefile{toc}{\contentsline {section}{\numberline {6}Sensitivity computation ingredients}{6}} |
---|
81 | \citation{MEZZETTONUFACT060} |
---|
82 | \citation{KAMLAND} |
---|
83 | \citation{JJG} |
---|
84 | \citation{MEZZETTONUFACT060} |
---|
85 | \citation{KAMLAND} |
---|
86 | \citation{JJG} |
---|
87 | \@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Integral of the different species fluxes with different settings. The $\nu _\mu $ and $\mathaccent "7016\relax {\nu }_\mu $ fluxes are expressed in $10^{13}/100\@mathrm {m}^2/y$ unit while the $\nu _e$ and $\mathaccent "7016\relax {\nu }_e$ fluxes are expressed in $10^{11}/100\@mathrm {m}^2/y$ unit. The positive focusing and negative focusing are distinguished by a ($+$) sign and a ($-$) sign, respectively. The settings used corresponds to different values of $L_T$ and $R_T$, the length and radius of the decay tunnel. Setting (1) is the baseline option and means $L_T = 20$\nobreakspace {}m and $R_T = 1$\nobreakspace {}m, while setting (2) means $L_T = 10$\nobreakspace {}m and $R_T = 1$\nobreakspace {}m and setting (3) means $L_T = 40$\nobreakspace {}m and $R_T = 1$\nobreakspace {}m, and finally the setting (4) means $L_T = 20$\nobreakspace {}m and $R_T = 1.5$\nobreakspace {}m.}}{7}} |
---|
88 | \newlabel{tab:speciesfluxes}{{5}{7}} |
---|
89 | \@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Neutrino fluxes $100$\nobreakspace {}km from the decay region and with the horns focusing the positive particles. The fluxes are computed for a SPL proton beam of $2.2$\nobreakspace {}GeV (4\nobreakspace {}MW), a decay tunnel with a length of $20$\nobreakspace {}m and a radius of $1$\nobreakspace {}m. The (\mbox {------}) curve is the contribution from primary pions and the daughter muons, the (\mbox {- - - -}) curve is the contribution from the charged kaon decay chain, and the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve is the contribution from the $K^0$ decay chain.}}{7}} |
---|
90 | \newlabel{fig:flux22p}{{6}{7}} |
---|
91 | \@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Same legend as for figure\nobreakspace {}6\hbox {} but the horns are focusing negative particles.}}{7}} |
---|
92 | \newlabel{fig:flux22m}{{7}{7}} |
---|
93 | \citation{MEZZETTONUFACT060} |
---|
94 | \@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Same legend as for figure\nobreakspace {}6\hbox {} but for proton beam kinetic energy of $4.5$\nobreakspace {}GeV (4\nobreakspace {}MW).}}{8}} |
---|
95 | \newlabel{fig:flux45p}{{8}{8}} |
---|
96 | \@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Same legend as for figure\nobreakspace {}7\hbox {} but for proton beam kinetic energy of $4.5$\nobreakspace {}GeV (4\nobreakspace {}MW).}}{8}} |
---|
97 | \newlabel{fig:flux45m}{{9}{8}} |
---|
98 | \@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Default user parameters used to compute the sensitivity curves \cite {MEZZETTONUFACT060}. The quoted errors in parenthesis for the $(12)$ and the $(23)$ parameters (absolute value for the masses and relative value for the angles) are coming respectively from the up to date combined Solar and KamLAND results \cite {KAMLAND} and from a 200 ktons-years SPL desappearance exposure \cite {JJG}.}}{8}} |
---|
99 | \newlabel{tab:param}{{6}{8}} |
---|
100 | \@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Same legend as for figure\nobreakspace {}6\hbox {} but for proton beam kinetic energy of $8$\nobreakspace {}GeV (4\nobreakspace {}MW).}}{8}} |
---|
101 | \newlabel{fig:flux8p}{{10}{8}} |
---|
102 | \@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Same legend as for figure\nobreakspace {}7\hbox {} but for proton beam kinetic energy of $8$\nobreakspace {}GeV (4\nobreakspace {}MW).}}{8}} |
---|
103 | \newlabel{fig:flux8m}{{11}{8}} |
---|
104 | \@writefile{toc}{\contentsline {section}{\numberline {7}Results}{8}} |
---|
105 | \newlabel{sec:results}{{7}{8}} |
---|
106 | \citation{DONINI} |
---|
107 | \citation{DONINI,JJG,Mezzetto} |
---|
108 | \@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Number of events for 5 years positive focusing scenario with default parameters of table\nobreakspace {}6\hbox {}. : $\pi ^0$, $\nu _\mu $-elast., $\mu /e$-missId. The significance parameter is defined by equation\nobreakspace {}1\hbox {}.}}{9}} |
---|
109 | \newlabel{tab:nbvsE}{{7}{9}} |
---|
110 | \@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces Minimum $\mathop {\mathgroup \symoperators sin}\nolimits ^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for diferent decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$). Other parameters are fixed to default values (table\nobreakspace {}6\hbox {}).}}{9}} |
---|
111 | \newlabel{tab:thvsE}{{8}{9}} |
---|
112 | \newlabel{eq:significance}{{1}{9}} |
---|
113 | \@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Sensitivity contours obtained with a SPL energy of $4.5$\nobreakspace {}GeV and default parameters of table\nobreakspace {}6\hbox {}.}}{9}} |
---|
114 | \newlabel{fig:sensi45}{{12}{9}} |
---|
115 | \@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Comparison of 90\% sensitivity contours obtained with SPL energies of ($2.2$, $3.5$, $4.5$, $8$)\nobreakspace {}GeV and default parameters of table\nobreakspace {}6\hbox {}.}}{9}} |
---|
116 | \newlabel{fig:compSensi}{{13}{9}} |
---|
117 | \@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Minimum $\mathop {\mathgroup \symoperators sin}\nolimits ^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for different level of systematics ($\epsilon _{syst}$) and kinetic beam energy ($E_k(proton)$). Other parameters are fixed to default values (table\nobreakspace {}6\hbox {}).}}{9}} |
---|
118 | \newlabel{tab:thvseps}{{9}{9}} |
---|
119 | \citation{GEANT4} |
---|
120 | \citation{DONINI} |
---|
121 | \@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces $90\%$ CL sensitivity contours obtained with a SPL energy of $4.5$\nobreakspace {}GeV and default parameters of table\nobreakspace {}6\hbox {} but for different $\epsilon _{syst}$ values.}}{10}} |
---|
122 | \newlabel{fig:compEpsSyst}{{14}{10}} |
---|
123 | \@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Minimum $\mathop {\mathgroup \symoperators sin}\nolimits ^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for different values of sign$(\Delta m^2_{23})$ and $\delta _{CP}$. Other parameters are fixed to default values (table\nobreakspace {}6\hbox {}).}}{10}} |
---|
124 | \newlabel{tab:sign}{{10}{10}} |
---|
125 | \@writefile{toc}{\contentsline {section}{\numberline {8}Summary and outlook}{10}} |
---|
126 | \@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Sensitivity contours obtained with SPL beam energy of $2.2$\nobreakspace {}GeV (\mbox {- - - -}), $3.5$\nobreakspace {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace {}GeV (\mbox {------}) and $8$\nobreakspace {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) at $90\%$ CL. Default parameters of table\nobreakspace {}6\hbox {} are used either with a 5 years positive focusing scenario (a) or a mixed scenario of 2 years positive focusing and 8 years of negative focusing (b).}}{10}} |
---|
127 | \newlabel{fig:compDeltaTheta}{{15}{10}} |
---|
128 | \citation{donega} |
---|
129 | \citation{Gaisser} |
---|
130 | \citation{picasso} |
---|
131 | \citation{pdg} |
---|
132 | \@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha $ is needed.}}{11}} |
---|
133 | \newlabel{fig:pionDecay}{{16}{11}} |
---|
134 | \@writefile{toc}{\contentsline {section}{\numberline {B}Decay probability computations}{11}} |
---|
135 | \newlabel{sec:decayprobcomp}{{B}{11}} |
---|
136 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.1}Pion neutrino probability computation}{11}} |
---|
137 | \newlabel{sec:Ppi}{{B.1}{11}} |
---|
138 | \newlabel{probaPi}{{2}{11}} |
---|
139 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.2}Muon neutrino probability computation}{11}} |
---|
140 | \newlabel{sec:Pmu}{{B.2}{11}} |
---|
141 | \@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Flux function in the muon rest frame \cite {Gaisser}.}}{11}} |
---|
142 | \newlabel{tab:Function}{{11}{11}} |
---|
143 | \@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Charged and neutral kaon decay channels \cite {pdg}.}}{11}} |
---|
144 | \newlabel{tab:BRKP0SL}{{12}{11}} |
---|
145 | \newlabel{probaMu}{{3}{11}} |
---|
146 | \newlabel{pola}{{4}{11}} |
---|
147 | \@writefile{toc}{\contentsline {subsection}{\numberline {B.3}The treatment of the kaons}{11}} |
---|
148 | \newlabel{sec:kaons}{{B.3}{11}} |
---|
149 | \bibcite{SKNU04}{1} |
---|
150 | \bibcite{K2KNU04}{2} |
---|
151 | \bibcite{MINOS}{3} |
---|
152 | \bibcite{OPERA}{4} |
---|
153 | \bibcite{ICARUS}{5} |
---|
154 | \bibcite{CNGS}{6} |
---|
155 | \bibcite{LSND}{7} |
---|
156 | \bibcite{MINIBOONE}{8} |
---|
157 | \bibcite{PMNS}{9} |
---|
158 | \bibcite{CHOOZ}{10} |
---|
159 | \bibcite{Wpaper}{11} |
---|
160 | \bibcite{BETABEAM}{12} |
---|
161 | \bibcite{NOVA}{13} |
---|
162 | \bibcite{T2K}{14} |
---|
163 | \bibcite{BNLHS}{15} |
---|
164 | \bibcite{CERN}{16} |
---|
165 | \bibcite{DONINI}{17} |
---|
166 | \bibcite{DOUBLE-CHOOZ}{18} |
---|
167 | \bibcite{SPL}{19} |
---|
168 | \bibcite{UNO}{20} |
---|
169 | \bibcite{mosca}{21} |
---|
170 | \bibcite{Meer}{22} |
---|
171 | \bibcite{nuFact134}{23} |
---|
172 | \bibcite{MMWPSCazes}{24} |
---|
173 | \bibcite{JJG}{25} |
---|
174 | \bibcite{Mezzetto}{26} |
---|
175 | \bibcite{nuFact138}{27} |
---|
176 | \bibcite{fluka}{28} |
---|
177 | \bibcite{MMWPSGaroby}{29} |
---|
178 | \bibcite{harp}{30} |
---|
179 | \bibcite{minerva}{31} |
---|
180 | \newlabel{probaL}{{5}{12}} |
---|
181 | \bibcite{MARS}{32} |
---|
182 | \bibcite{FLUKAprivate}{33} |
---|
183 | \bibcite{geant}{34} |
---|
184 | \bibcite{SIMONE1}{35} |
---|
185 | \bibcite{donega}{36} |
---|
186 | \bibcite{DONINI-2}{37} |
---|
187 | \bibcite{NUANCE}{38} |
---|
188 | \bibcite{MEZZETTONUFACT060}{39} |
---|
189 | \bibcite{KAMLAND}{40} |
---|
190 | \bibcite{Gaisser}{41} |
---|
191 | \bibcite{picasso}{42} |
---|
192 | \bibcite{pdg}{43} |
---|
193 | \bibcite{GEANT4}{44} |
---|