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2 | \subsection{SPL SuperBeam} |
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3 | % -------------------------- |
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4 | %In the CERN-SPL SuperBeam project \cite{SPL,SPL-Physics,nufact1} |
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5 | % the planned 4MW SPL (Superconducting Proton Linac) would deliver a 2.2 GeV/c |
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6 | % proton beam, on a Hg target to generate |
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7 | % an intense $\pi^+$ ($\pi^-$) beam focused by a suitable |
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8 | % magnetic horn in a short decay tunnel. As a result an intense |
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9 | % $\nu_{\mu}$ beam, will be produced |
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10 | % mainly via the $\pi$-decay, $\pi^+ \rightarrow \nu_{\mu} \; \mu^+$ providing a |
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11 | % flux $\phi \sim 3.6 {\cdot} 10^{11} \nu_{\mu}$/year/m$^2$ at 130 Km |
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12 | % of distance, and an average energy of 0.27 GeV. |
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13 | % The $\nu_e$ contamination from $K$ will be suppressed by threshold effects |
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14 | % and the resulting $\nu_e/\nu_{\mu}$ ratio ($ \sim 0.4 \%$) |
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15 | % will be known within $2\%$ error. |
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16 | % The use of a near and far detector (the latter at $L = 130$ Km of distance |
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17 | % in the Frejus area \cite{Mosca}) |
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18 | % will allow for both $\nu_{\mu}$-disappearance and |
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19 | % $\nu_{\mu} \rightarrow \nu_e$ appearance studies. |
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20 | % The physics potential of the 2.2 GeV SPL SuperBeam (SPL-SB) |
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21 | % with a water Cerenkov far detector fiducial mass of 440 Kt \cite{UNO} has been extensively |
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22 | % studied \cite{SPL-Physics}. \\ |
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23 | % |
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24 | % New developments show that the potential of the SPL-SB potential could be |
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25 | % improved by rising the SPL energy to 3.5 GeV \cite{Cazes}, |
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26 | % to produce more copious secondary mesons |
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27 | % and to focus them more efficiently. This seems feasible if |
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28 | % status of the art RF cavities would be used in place of the old foreseen LEP cavities |
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29 | % \cite{Garoby-SPL}. |
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30 | % In this upgraded configuration neutrino flux could be increased by a factor 3 with |
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31 | % with respect to the 2.2 GeV configuration, reaching |
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32 | % a sensitivity to $\sin^2{2 \thetaot}$ 8 times better than T2K and allowing |
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33 | % to discovery CP violation (at 3 $\sigma$ level) if |
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34 | % $\delCP \geq 25^\circ$ and |
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35 | % $\theta_{13} \geq 1.4^\circ$ \cite{MMNufact04}. The expected |
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36 | % performances are shown in Fig.~\ref{fig:th13}. |
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37 | % |
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38 | % \begin{figure} |
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39 | % \centerline{\epsfig{file=show_fluxes_new.eps,width=0.5\textwidth}} |
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40 | % \mycaption{Neutrino flux of $\beta$-Beam ($\gamma=100$) |
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41 | % and CERN-SPL SuperBeam, 3.5 GeV, at 130 Km of distance.} |
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42 | % \label{fig:fluxes} |
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43 | % \end{figure} |
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44 | |
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45 | An optimization of the energy as well as the secondary particle focusing and decay tunnel has been undertaken in the context of a Super Beam of 4~MW \cite{JECACLAL} using the CERN-SPL \cite{SPL} and searching for $\nu_\mu \rightarrow \nu_e$ ($\bar{\nu}_\mu \rightarrow \bar{\nu}_e$) appearance channels in an 500~kT fiducial volume water Cerenkov detector, called MEMPHYS, and located in an possible new underground laboratory at the Fréjus tunnel, 130~km from the CERN complex. The use of a near detector will also enable the use of the disappearance channels. |
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46 | |
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47 | The secondary particles from the interaction of proton beam impinging a 30~cm long 1.5~cm diameter mercury target, have been obtained with the FLUKA generator (see Tab.~\ref{tab:nbPart}). At kinetic energy of 3.5 (2.2)~GeV, the number of p.o.t per year is 0.69 (1.10) $10^{23}$ while the numbers of $\pi^+/\pi^-/K^+/K^o$ per p.o.t are $0.41/0.37/35 10^{-4}/30 10^{-4}$ ($0.24/0.18/7 10^{-4}/6 10^{-4}$). At higher beam energy, the kaon rates grow rapidly compared to the pion rates, and needless to emphasize the need of an experimental confirmation \cite{HARP,MINERVA} of such numbers. |
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48 | |
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49 | The focusing system (magnetic horns) optimized in the context of a Neutrino Factory \cite{SIMONE1,DONEGA} has been redesigned considering the specific requirements of a Super Beam. The most important points are the phase spaces that are covered by the two types of horns are different, and that for a Super Beam the pions to be focused should have an energy of the order of $p_\pi (\mathrm{MeV})/3 \approx E_\nu \gtrsim 2L(\mathrm{km})$ to obtain a maximum oscillation probability. In practice, this means that one should collect $800$~MeV/c pions to get a mean neutrino energy of $300$~MeV. |
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50 | |
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51 | \begin{table} |
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52 | \centering |
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53 | \caption{\label{tab:nbPart}Average numbers of the most relevant secondary particles exiting the $30$~cm long, $1.5$~cm diameter mercury target per incident proton (FLUKA).} |
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54 | \begin{tabular}{@{}l*{15}{l}} |
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55 | \hline\noalign{\smallskip} |
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56 | $E_k$ (GeV) & p.o.t/y & $\pi^+$ & $\pi^-$ & $K^+$ & $K^0$ \\ |
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57 | & $\times 10^{23}$ & & & \multicolumn{2}{c}{$\times 10^{-4}$} \\ |
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58 | \noalign{\smallskip}\hline\noalign{\smallskip} |
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59 | $2.2$ & $1.10$ & $0.24$ & $0.18$ & $7$ & $6$ \\ |
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60 | $3.5$ & $0.69$ & $0.41$ & $0.37$ & $35$ & $30$ \\ |
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61 | $4.5$ & $0.54$ & $0.57$ & $0.39$ & $93$ & $68$ \\ |
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62 | $8.0$ & $0.30$ & $1.00$ & $0.85$ & $413$ & $340$ \\ |
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63 | \noalign{\smallskip}\hline |
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64 | \end{tabular} |
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65 | \end{table} |
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66 | |
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67 | The resulting fluxes for the positive ($\nu_\mu$ beam) and the negative focusing ($\bar{\nu}_\mu$ beam) are show on figure \ref{fig:fluxComparison}. The total number of $\nu_\mu$ ($\bar{\nu}_\mu$) in positive (negative) focusing is about $1.18 (0.97) 10^{12}/\mathrm{m}^2/\mathrm{yr}$ with an average energy of $300$~MeV. The $\nu_e$ ($\bar{\nu}_\mu$) contamination in the $\nu_\mu$ beam is around $0.7\%$ ($6.0\%$) |
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68 | and will be known within $2\%$ error. Compared to the fluxes used in references \cite{MEZZETTONF02,DONINI04} the gain is at least a factor $2.5$. Using neutrino cross-sections on water \cite{LIPARIxsec}, the number of expected $\nu_\mu$ charged current is about $95$ per kT.yr. |
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69 | % |
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70 | \begin{figure} |
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71 | \centering |
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72 | \includegraphics[height=60mm]{OptiVsOldFlux.eps} |
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73 | \caption{\label{fig:fluxComparison}The $\nu_\mu$ and the $\bar{\nu}_\mu$ fluxes obtained by optimizing the SPL for a Super Beam case ("SB Opt.") are compared to those obtained with a focusing system designed for a Neutrino Factory ("NF Opt.").} |
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74 | \end{figure} |
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75 | |
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76 | The physics potential of the new optimized SPL may be determined using GLoBES software \cite{GLOBES}. Both the appearance and the disappearance channels have been used, and also five bins of 200~MeV each have been introduced. The $\pi^o$ background have been rejected using a tighter PID cut compared to standard SuperK analysis \cite{MEZZETTONF02}. The Michel electron has been required for the $\mu$ identification. As ultimate goal suggested by \cite{T2K} a 2\% systematical error is used both for signal and background. |
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77 | |
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78 | The $90\%$ CL sensitivity contour in the ($\Delta m^2_{31}$,$\sin^22\theta_{13}$) plane after 5 years running with a positive focusing is shown on figure \ref{fig:SPLDmTheta13Comparison}. With the new optimized setup, one expects to reach a limit on $\theta_{13}$ of $0.7^o$. |
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79 | % |
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80 | \begin{figure} |
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81 | \centering |
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82 | \includegraphics[height=60mm]{compareOldNewthetaDm.eps} |
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83 | \caption{\label{fig:SPLDmTheta13Comparison}Comparison of the sensitivity contours with the new optimized setup and the original SPL design after 5 years of running with positive focusing.} |
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84 | \end{figure} |
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85 | % |
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86 | One may also appreciate on figure \ref{fig:SPLCPSensi} the improvement on the combined sensitivity of $\sin^22\theta_{13}$ and $\delta_{CP}$ with the new optimization compared for instance to the T2K project \cite{T2K}. |
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87 | % |
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88 | \begin{figure} |
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89 | \centering |
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90 | \includegraphics[height=60mm]{deltaThetaSens5yOldNew.eps} |
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91 | \caption{\label{fig:SPLCPSensi}Comparison of the sensitivity on combined $\theta_{13}$ and $\delta_{CP}$ after 5 years of positive focusing. The T2K sensitivity contour has been derived from reference \cite{T2K}. No mass hierarchy nor octant hierarchy ambiguity has been considered.} |
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92 | \end{figure} |
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93 | % |
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94 | |
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95 | So, the optimized SPL beam line operating a Super Beam towards a megaton scale detector (called MEMPHYS) at the Fréjus tunnel has a great potential. |
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96 | |
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97 | |
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98 | %%%%%%%%%%%%%%%%%%%% SPL Bibliography %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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99 | |
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100 | \bibitem{JECACLAL} |
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101 | J.E Campagne and A. Cazes, LAL-04-102, arXiv:hep-ex/405002 submitted to \EJP |
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102 | |
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103 | \bibitem{SPL} |
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104 | SPL Conceptual Design, CERN 2000-012 |
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105 | |
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106 | \bibitem{HARP} |
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107 | C. Catanesi \etal, CERN-SPSC 2002/019 |
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108 | |
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109 | \bibitem{MINERVA} |
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110 | D. Drakoulakos \etal, Fermilab P-938, arXiv:hep-ex/405002 |
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111 | |
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112 | \bibitem{SIMONE1} |
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113 | S.~Gilardoni \etal, AIP Conf.\ Proc.\ {\bf 721} (2004) 334. |
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114 | |
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115 | \bibitem{DONEGA} |
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116 | A. Blondel \etal, CERN-NUFACT-Note-78 (2001) |
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117 | |
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118 | \bibitem{MEZZETTONF02} |
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119 | M. Mezzetto, \jpg {\bf 29}, 1781-1784 (2003), arXiv:hep-ex/0302005 |
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120 | |
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121 | \bibitem{DONINI04} |
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122 | A. Donini \etal, IFT-UAM/CSIC-04-30 (2004), arXiv:hep-ph/0406132 |
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123 | |
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124 | \bibitem{LIPARIxsec} |
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125 | P.~Lipari, M.~Lusignoli and F.~Sartogo, |
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126 | %``The Neutrino cross-section and upward going muons,'' |
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127 | \PRL {\bf 74} (1995) 4384, arXiv:hep-ph/9411341 |
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128 | |
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129 | \bibitem{GLOBES} |
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130 | P. Hubert, M. Lindner and W. Winter, arXiv:hep-ph/0407333, |
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131 | Comput.Phys.Commun. 167 (2005) 195. |
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132 | |
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133 | \bibitem{T2K} |
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134 | T. Kobayashi, \NP B 143 (Proc. Supp.) (2005) 303 |
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135 | |
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136 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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137 | |
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138 | |
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