\relax 
\citation{SKNU04,K2KNU04}
\citation{K2KNU04}
\citation{MINOS}
\citation{OPERA,ICARUS}
\citation{CNGS}
\citation{LSND}
\citation{MINIBOONE}
\citation{PMNS}
\citation{CHOOZ}
\citation{Wpaper}
\citation{BETABEAM}
\citation{NOVA,T2K}
\citation{T2K,BNLHS,CERN}
\citation{CERN}
\citation{DONINI}
\citation{DONINI,DOUBLE-CHOOZ}
\citation{SPL}
\citation{UNO}
\citation{mosca}
\citation{CERN}
\citation{Meer}
\citation{nuFact134,MMWPSCazes}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Sketch of the SPL neutrino Superbeam from CERN to the Fr\'ejus tunnel.}}{2}}
\newlabel{fig:Sbeam}{{1}{2}}
\citation{DONINI,JJG,Mezzetto}
\citation{nuFact138}
\citation{fluka}
\citation{CERN}
\citation{SPL}
\citation{MMWPSGaroby}
\citation{nuFact134}
\citation{harp}
\citation{minerva}
\citation{MARS}
\citation{nuFact134}
\citation{MMWPSGaroby}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Liquid mercury jet parameters.}}{3}}
\newlabel{tab:targ}{{1}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Target simulation}{3}}
\newlabel{sec:target}{{2}{3}}
\@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}}
\newlabel{fig:compFlukaMars}{{2}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Kaon production}{3}}
\newlabel{sec:kaon}{{3}{3}}
\citation{FLUKAprivate}
\citation{geant}
\citation{SIMONE1}
\citation{nuFact138}
\@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}}
\newlabel{tab:nbPart}{{2}{4}}
\@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}}
\newlabel{fig:KaonsPions}{{3}{4}}
\@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}}
\newlabel{tab:specif}{{3}{4}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Horn simulation}{4}}
\newlabel{sec:horn}{{4}{4}}
\citation{donega}
\citation{donega}
\citation{donega}
\@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}}
\newlabel{fig:plan}{{4}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Particle decay treatment and flux calculation}{5}}
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Number of protons on target for different beam energy at 4\nobreakspace  {}MW constant power.}}{5}}
\newlabel{tab:proton}{{4}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Algorithm description}{5}}
\newlabel{sec:algo}{{5.1}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Validation of the algorithm}{5}}
\citation{donega}
\citation{MEZZETTONUFACT060}
\citation{DONINI-2}
\citation{NUANCE}
\citation{MEZZETTONUFACT060}
\citation{UNO}
\citation{mosca}
\@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}}
\newlabel{fig:compGeantDonega}{{5}{6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Simulated fluxes}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Sensitivity computation ingredients}{6}}
\citation{MEZZETTONUFACT060}
\citation{KAMLAND}
\citation{JJG}
\citation{MEZZETTONUFACT060}
\citation{KAMLAND}
\citation{JJG}
\@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}}
\newlabel{tab:speciesfluxes}{{5}{7}}
\@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}}
\newlabel{fig:flux22p}{{6}{7}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but the horns are focusing negative particles.}}{7}}
\newlabel{fig:flux22m}{{7}{7}}
\citation{MEZZETTONUFACT060}
\@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}}
\newlabel{fig:flux45p}{{8}{8}}
\@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}}
\newlabel{fig:flux45m}{{9}{8}}
\@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}}
\newlabel{tab:param}{{6}{8}}
\@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}}
\newlabel{fig:flux8p}{{10}{8}}
\@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}}
\newlabel{fig:flux8m}{{11}{8}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Results}{8}}
\newlabel{sec:results}{{7}{8}}
\citation{DONINI}
\citation{DONINI,JJG,Mezzetto}
\@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}}
\newlabel{tab:nbvsE}{{7}{9}}
\@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}}
\newlabel{tab:thvsE}{{8}{9}}
\newlabel{eq:significance}{{1}{9}}
\@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}}
\newlabel{fig:sensi45}{{12}{9}}
\@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}}
\newlabel{fig:compSensi}{{13}{9}}
\@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}}
\newlabel{tab:thvseps}{{9}{9}}
\citation{GEANT4}
\citation{DONINI}
\@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}}
\newlabel{fig:compEpsSyst}{{14}{10}}
\@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}}
\newlabel{tab:sign}{{10}{10}}
\@writefile{toc}{\contentsline {section}{\numberline {8}Summary and outlook}{10}}
\@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}}
\newlabel{fig:compDeltaTheta}{{15}{10}}
\citation{donega}
\citation{Gaisser}
\citation{picasso}
\citation{pdg}
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha $ is needed.}}{11}}
\newlabel{fig:pionDecay}{{16}{11}}
\@writefile{toc}{\contentsline {section}{\numberline {B}Decay probability computations}{11}}
\newlabel{sec:decayprobcomp}{{B}{11}}
\@writefile{toc}{\contentsline {subsection}{\numberline {B.1}Pion neutrino probability computation}{11}}
\newlabel{sec:Ppi}{{B.1}{11}}
\newlabel{probaPi}{{2}{11}}
\@writefile{toc}{\contentsline {subsection}{\numberline {B.2}Muon neutrino probability computation}{11}}
\newlabel{sec:Pmu}{{B.2}{11}}
\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Flux function in the muon rest frame \cite  {Gaisser}.}}{11}}
\newlabel{tab:Function}{{11}{11}}
\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Charged and neutral kaon decay channels \cite  {pdg}.}}{11}}
\newlabel{tab:BRKP0SL}{{12}{11}}
\newlabel{probaMu}{{3}{11}}
\newlabel{pola}{{4}{11}}
\@writefile{toc}{\contentsline {subsection}{\numberline {B.3}The treatment of the kaons}{11}}
\newlabel{sec:kaons}{{B.3}{11}}
\bibcite{SKNU04}{1}
\bibcite{K2KNU04}{2}
\bibcite{MINOS}{3}
\bibcite{OPERA}{4}
\bibcite{ICARUS}{5}
\bibcite{CNGS}{6}
\bibcite{LSND}{7}
\bibcite{MINIBOONE}{8}
\bibcite{PMNS}{9}
\bibcite{CHOOZ}{10}
\bibcite{Wpaper}{11}
\bibcite{BETABEAM}{12}
\bibcite{NOVA}{13}
\bibcite{T2K}{14}
\bibcite{BNLHS}{15}
\bibcite{CERN}{16}
\bibcite{DONINI}{17}
\bibcite{DOUBLE-CHOOZ}{18}
\bibcite{SPL}{19}
\bibcite{UNO}{20}
\bibcite{mosca}{21}
\bibcite{Meer}{22}
\bibcite{nuFact134}{23}
\bibcite{MMWPSCazes}{24}
\bibcite{JJG}{25}
\bibcite{Mezzetto}{26}
\bibcite{nuFact138}{27}
\bibcite{fluka}{28}
\bibcite{MMWPSGaroby}{29}
\bibcite{harp}{30}
\bibcite{minerva}{31}
\newlabel{probaL}{{5}{12}}
\bibcite{MARS}{32}
\bibcite{FLUKAprivate}{33}
\bibcite{geant}{34}
\bibcite{SIMONE1}{35}
\bibcite{donega}{36}
\bibcite{DONINI-2}{37}
\bibcite{NUANCE}{38}
\bibcite{MEZZETTONUFACT060}{39}
\bibcite{KAMLAND}{40}
\bibcite{Gaisser}{41}
\bibcite{picasso}{42}
\bibcite{pdg}{43}
\bibcite{GEANT4}{44}