source: Backup NB/Talks/MEMPHYSetal/SPLFrejusArt/SPLFrejusEPJC/SPLFrejusv3r2.aux @ 392

\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}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Sketch of the SPL neutrino Superbeam from CERN to the Fr\'ejus tunnel.}}{1}}
\newlabel{fig:Sbeam}{{1}{1}}
\citation{nuFact134,MMWPSCazes}
\citation{DONINI,JJG,Mezzetto}
\citation{nuFact138}
\citation{fluka}
\citation{CERN}
\citation{JJG}
\citation{CERN}
\citation{SPL}
\citation{MMWPSGaroby}
\citation{nuFact134}
\citation{harp}
\citation{MARS}
\citation{nuFact134}
\citation{MMWPSGaroby}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Liquid mercury jet parameters.}}{2}}
\newlabel{tab:targ}{{1}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Target simulation}{2}}
\newlabel{sec:target}{{2}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Kaon production}{2}}
\newlabel{sec:kaon}{{3}{2}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  (a) $\pi ^+$ momentum distribution per second at the exit of the target for the different proton beam energies studied, simulated with FLUKA, and (b) $\pi ^+$ angle with respect to the beam axis of the pion having a momentum between $0.5$\nobreakspace  {}GeV/c and $0.7$\nobreakspace  {}GeV/c. The different SPL beam kinetic energies presented are (\mbox {------}) $2.2$\nobreakspace  {}GeV, (\mbox {- - - -}) $3.5$\nobreakspace  {}GeV, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) $4.5$\nobreakspace  {}GeV and (\mbox {--- $\cdot $ ---}) $6.5$\nobreakspace  {}GeV.}}{3}}
\newlabel{fig:compEner2}{{2}{3}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces $\pi ^+$ momentum distribution at the exit of the target (a) and at the exit of the horns (b), simulated by FLUKA (\mbox {- - - -}) and by MARS (\mbox {------}).}}{3}}
\newlabel{fig:compFlukaMars}{{3}{3}}
\citation{FLUKAprivate}
\citation{geant}
\citation{SIMONE1}
\citation{nuFact138}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Average numbers 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{toc}{\contentsline {section}{\numberline {4}Horns simulation}{4}}
\newlabel{sec:horn}{{4}{4}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Relevant parameters of the horns in case of the generation of a $260$\nobreakspace  {}MeV neutrino beam (or $350$\nobreakspace  {}MeV in paranthesis). The shapes of the conductors are independent of the proton beam energy, as the focusing has been optimized for a $600$\nobreakspace  {}MeV/c (or $800$\nobreakspace  {}MeV/c) pion momentum.}}{4}}
\newlabel{tab:specif}{{3}{4}}
\citation{donega}
\citation{donega}
\citation{donega}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  Kaon production (left panel) and pion production (right panel) defined as number of particle produced per proton on target (p.o.t) as function of the kinetic energy of the incident proton ($E_k$).}}{5}}
\newlabel{fig:KaonsPions}{{4}{5}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Design of the Horn and the Reflector conductors implemented in the GEANT simulation in case of the generation of a 350\nobreakspace  {}MeV neutrino beam. The Hg target is located inside the cylindrical part of the Horn.}}{5}}
\newlabel{fig:plan}{{5}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Particle decay treatment and flux calculation}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Algorithm description}{5}}
\newlabel{sec:algo}{{5.1}{5}}
\citation{donega}
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces Number of protons on target for different beam energy at 4\nobreakspace  {}MW constant power. One year is defined as $10^7$\nobreakspace  {}s.}}{6}}
\newlabel{tab:proton}{{4}{6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Validation of the algorithm}{6}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Simulated fluxes}{6}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  Neutrino fluxes, $100$\nobreakspace  {}km from the target 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 top left panel contains the $\nu _\mu $ fluxes, and the top right panel shows the $\mathaccentV {bar}016{\nu }_\mu $ fluxes. The bottom left panel presents the $\nu _e$ fluxes while the bottom right panel displays the $\mathaccentV {bar}016{\nu }_e$ fluxes. The (\mbox {------}) curve is the contribution from primary pions and the daughter muons, and from primary 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. An insert has been added to the plots to hight light when needed the contribution of charged and neutral kaons.}}{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}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Same legend as for figure\nobreakspace  {}6\hbox {} but for proton beam kinetic energy of $3.5$\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 $3.5$\nobreakspace  {}GeV (4\nobreakspace  {}MW).}}{8}}
\newlabel{fig:flux45m}{{9}{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).}}{9}}
\newlabel{fig:flux8p}{{10}{9}}
\@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).}}{9}}
\newlabel{fig:flux8m}{{11}{9}}
\citation{UNO}
\citation{JJG}
\citation{MEZZETTONUFACT060}
\citation{Mezzetto}
\citation{DONINI-2}
\citation{NUANCE}
\citation{MEZZETTONUFACT060}
\citation{mosca}
\citation{MEZZETTONUFACT060}
\citation{KAMLAND}
\citation{JJG}
\citation{MEZZETTONUFACT060}
\citation{KAMLAND}
\citation{JJG}
\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Integral of the total flux of the different species with different settings. The $\nu _\mu $ and $\mathaccentV {bar}016{\nu }_\mu $ fluxes are expressed in $10^{13}/100\@mathrm {m}^2/y$ unit while the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ 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. }}{10}}
\newlabel{tab:speciesfluxes}{{5}{10}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Sensitivity computation ingredients}{10}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Results}{10}}
\newlabel{sec:results}{{7}{10}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}The positive only focusing scenario}{10}}
\citation{DONINI}
\citation{DONINI,JJG,Mezzetto}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Comparison between the probability method, (\mbox {------}) curve, and the full GEANT simulation method, (\mbox {- - - -}) curve, for the $\nu _\mu $ from $\pi ^+$ flux (a) and the $\mathaccentV {bar}016{\nu }_\mu $ from $\pi ^-$ flux (b). The horns are set to focus positive particles. It should be stressed that the full GEANT simulation has taken roughly 13 times more CPU time than the probability method with the same number of protons on target, and the later simulation is able to produce as well the $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ fluxes contrary to the former simulation.}}{11}}
\newlabel{fig:compGeantDonega}{{12}{11}}
\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Default 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 masse square differences 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}.}}{11}}
\newlabel{tab:param}{{6}{11}}
\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Number of events for 5 years positive focusing scenario with default parameters of table\nobreakspace  {}6\hbox {}. Other backgrounds are $\pi ^0$, $\nu _\mu $-elast., $\mu /e$-missId. }}{12}}
\newlabel{tab:nbvsE}{{7}{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Sensitivity contours obtained with a SPL energy of $3.5$\nobreakspace  {}GeV and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m. (\mbox {------}), (\mbox {- - - -}) and (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curves stand for $90\%$, $95\%$ and $99\%$ confidence level, respectively.}}{12}}
\newlabel{fig:sensi45}{{13}{12}}
\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different decay tunnel length ($L_T$) and kinetic beam energy ($E_k(proton)$) and 5 year of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{12}}
\newlabel{tab:thvsE}{{8}{12}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Mixed positive/negative focusing scenario}{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $2.2$\nobreakspace  {}GeV (\mbox {- - - -}), $3.5$\nobreakspace  {}GeV (\mbox {--- $\cdot $ ---}), $4.5$\nobreakspace  {}GeV (\mbox {------}) and $8$\nobreakspace  {}GeV (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) and default parameters of table\nobreakspace  {}6\hbox {}. In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{12}}
\newlabel{fig:compSensi}{{14}{12}}
\citation{CHOOZ}
\citation{Wpaper}
\citation{MIGLIOZZITERANOVA}
\citation{KOBAYASHI}
\citation{BNL}
\citation{MAOROPRIVATE}
\citation{CHOOZ}
\citation{Wpaper}
\citation{MIGLIOZZITERANOVA}
\citation{KOBAYASHI}
\citation{BNL}
\citation{MAOROPRIVATE}
\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces Study of the sensitivity of different beam energy, decay tunnel length ($L_T$) at and radius ($R_T$), and horn design in two different scenarios. First scenario is 5 years of positive focusing, in wich sensitivity is given as the minimum of $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL ($\delta _{CP} = 0$). Second scenario is 2 years of positive focusing plus 8 years of negative focusing, in wich sensitivity is given as the minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ observable at $90\%$ CL computed for the worse $\delta _{CP}$ case. A star $^{(*)}$ indicates the use of the the horn geometry producing a $350$\nobreakspace  {}MeV neutrino beam. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
\newlabel{tab:thvsE_3545}{{9}{13}}
\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Comparison of 90\% CL sensitivity contours obtained with SPL energies of $3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV, and either a $260$\nobreakspace  {}MeV (default) neutrino beam or a $350$\nobreakspace  {}MeV neutrino beam. The tunnel geometry parameters are $L_T = 40$\nobreakspace  {}m and $R_T = 2$\nobreakspace  {}m. The (\mbox {--- $\cdot $ ---}) curve corresponds to a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV (neutrino beam/SPL beam energy) setting; the (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve corresponds to a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting; the (\mbox {- - - -}) curve corresponds to a $260$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting and the (\mbox {------}) curve corresponds to a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting.}}{13}}
\newlabel{fig:comp5year}{{15}{13}}
\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for different level of systematics ($\epsilon _{syst}$) and kinetic beam energy ($E_k(proton)$) and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
\newlabel{tab:thvseps}{{10}{13}}
\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces Minimum $\qopname  \relax o{sin}^22\theta _{13}\times 10^3$ in the $(\qopname  \relax o{sin}^22\theta _{13},\Delta m^2_{23})$ plane observable at $90\%$ CL computed for a $2.2$\nobreakspace  {}GeV kinetic energy proton beam, and for different values of sign$(\Delta m^2_{23})$ and $\delta _{CP}$ and 5 years of positive focusing. Other parameters are fixed to default values (table\nobreakspace  {}6\hbox {}).}}{13}}
\newlabel{tab:sign}{{11}{13}}
\@writefile{toc}{\contentsline {section}{\numberline {8}Summary and outlook}{13}}
\citation{GEANT4}
\citation{BIGICARUS}
\citation{DONINI}
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces 90\% 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). In particular, it is reminded that the tunnel geometry parameters are $L_T = 20$\nobreakspace  {}m and $R_T = 1$\nobreakspace  {}m.}}{14}}
\newlabel{fig:compDeltaTheta}{{16}{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces 90\% CL sensitivity contours obtained with the decay tunnel geometry parameters $L_T=40$\nobreakspace  {}m and $R_T=2$\nobreakspace  {}m and different SPL beam energies ($3.5$\nobreakspace  {}GeV or $4.5$\nobreakspace  {}GeV) and different horn designs ($260$\nobreakspace  {}MeV or $350$\nobreakspace  {}MeV neutrino beams): (\mbox {------}) curve for a $350$\nobreakspace  {}MeV/$4.5$\nobreakspace  {}GeV setting, (\mbox {${\mathinner {\cdotp \cdotp \cdotp \cdotp \cdotp \cdotp }}$}) curve for a $350$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting, (\mbox {- - - -}) curve for a $260$\nobreakspace  {}MeV/$3.5$\nobreakspace  {}GeV setting. Other 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).}}{14}}
\newlabel{fig:sensiDeltaTheta}{{17}{14}}
\@writefile{toc}{\contentsline {section}{\numberline {A}Decay probability computations}{14}}
\newlabel{sec:decayprobcomp}{{A}{14}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A.1}Pion neutrino probability computation}{14}}
\newlabel{sec:Ppi}{{A.1}{14}}
\newlabel{probaPi}{{1}{14}}
\citation{donega}
\citation{Gaisser}
\citation{picasso}
\citation{pdg}
\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces 90\%CL sensitivity contours labeled by the project or experiment involved. The "CHOOZ excluded" dashed curve comes from the exclusion obtained from reference \cite  {CHOOZ} with $\Delta m^2 = \Delta m^2_{atm}$; in the same conditions is given the sensitivity foreseen for the "Double-CHOOZ" project \cite  {Wpaper}. The "CNGS combined" has been obtained combining the results form OPERA and ICARUS \cite  {MIGLIOZZITERANOVA}. The T2K contour has been derived from reference \cite  {KOBAYASHI}. The BNL contour has been obtained from reference \cite  {BNL}. The "Beta Beam" contour has been computed with 5 years running with both $\nu _e$ and $\mathaccentV {bar}016{\nu }_e$ neutrino beams in an appearance mode, while the dashed "Beta Beam disappearance" has been obtained as if the $\beta $ beam was analysed like a reactor experiment with 1\% systematic error \cite  {MAOROPRIVATE}. The "SPL 5y" and "SPL 2y+8y" and "SPL 1y+4y" curves have been obtained from the optimisation described in this paper ("5y": positive only focusing scenario; "1y+4y": 1 year of positive focusing and 4 years of negative focusing scenario; "2y+8y": 2 years of positive focusing and 8 years of negative focusing scenario) using a $3.5$\nobreakspace  {}GeV beam and a decay tunnel of $40$\nobreakspace  {}m length, and $2$\nobreakspace  {}m radius.}}{15}}
\newlabel{fig:deltathetaFinal}{{18}{15}}
\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Pion decay in the tunnel frame. To reach the detector, $\delta = -\alpha $ is needed.}}{15}}
\newlabel{fig:pionDecay}{{19}{15}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A.2}Muon neutrino probability computation}{15}}
\newlabel{sec:Pmu}{{A.2}{15}}
\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces Flux function in the muon rest frame \cite  {Gaisser}.}}{15}}
\newlabel{tab:Function}{{12}{15}}
\newlabel{probaMu}{{2}{15}}
\newlabel{pola}{{3}{15}}
\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}
\@writefile{lot}{\contentsline {table}{\numberline {13}{\ignorespaces Charged and neutral kaon decay channels \cite  {pdg}.}}{16}}
\newlabel{tab:BRKP0SL}{{13}{16}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A.3}The treatment of the kaons}{16}}
\newlabel{sec:kaons}{{A.3}{16}}
\newlabel{probaL}{{4}{16}}
\bibcite{Mezzetto}{26}
\bibcite{nuFact138}{27}
\bibcite{fluka}{28}
\bibcite{MMWPSGaroby}{29}
\bibcite{harp}{30}
\bibcite{minerva}{31}
\bibcite{MARS}{32}
\bibcite{FLUKAprivate}{33}
\bibcite{geant}{34}
\bibcite{SIMONE1}{35}
\bibcite{donega}{36}
\bibcite{MEZZETTONUFACT060}{37}
\bibcite{DONINI-2}{38}
\bibcite{NUANCE}{39}
\bibcite{KAMLAND}{40}
\bibcite{MIGLIOZZITERANOVA}{41}
\bibcite{KOBAYASHI}{42}
\bibcite{BNL}{43}
\bibcite{MAOROPRIVATE}{44}
\bibcite{GEANT4}{45}
\bibcite{BIGICARUS}{46}
\bibcite{Gaisser}{47}
\bibcite{picasso}{48}
\bibcite{pdg}{49}