1 | \section{Neutrinos from reactors} |
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2 | \label{sec:Reactor} |
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3 | %\REDBLA{Version 0 by JEC 2/3/06} |
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4 | %\REDBLA{updated by A. Bueno 23/3/06} |
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5 | %\REDBLA{updated by JEC 16/10/06: this is a section now} |
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6 | %\REDBLA{updated by JEC 20/10/06} |
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7 | %\REDBLA{updated by JEC 24/10/06} |
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8 | % |
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9 | %T. Marrodan Undagoitia 10/12/06 START Small corrections |
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10 | %\REDBLA{ |
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11 | The KamLAND 1~kT liquid scintillator detector located at Kamioka in |
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12 | Japan had measured the flux of 53 power reactors corresponding to |
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13 | 701~Joule/cm${}^{2}$ \cite{Araki:2004mb}. An event rate of |
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14 | $365.2\pm23.7$ above 2.6~MeV for an exposure of 766~ton.y from this |
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15 | nuclear power reactors was expected. The observed rate was 258 events |
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16 | with a total of background of $17.8\pm7.3$. The clear deficit |
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17 | interpreted in terms of neutrino oscillation enables a measurement |
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18 | of $\theta_{12}$, the neutrino 1-2 family mixing angle |
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19 | ($\sin^2\theta_{12} = 0.31^{+0.02}_{-0.03}$) as well as the mass |
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20 | squared difference $\Delta m^2_{12} = 7.9\pm0.3~10^{-5}$eV${}^2$ |
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21 | (error quoted at $1~\sigma$). |
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22 | |
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23 | Future precision measurements are currently been |
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24 | investigated. Running KamLAND |
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25 | for 2-3 more years would gain 30\% (4\%) reduction in the spread of |
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26 | $\Delta m^2_{12}$ ($\theta_{12}$). |
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27 | %JEC 20/10/06 START include text from Schwetz & Petcov {Petcov:2006gy} |
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28 | Although it has been shown in sections \ref{sec:SN} and \ref{sec:Geo} |
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29 | that $\bar{\nu}_e$ originated from nuclear reactors can be a serious |
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30 | background for diffuse supernova neutrino and geoneutrino detections, |
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31 | the Fréjus site can take benefit of the nuclear reactors located in |
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32 | the Rh\^one valley to measure $\Delta m_{21}^2$ and $\sin^2\theta_{12}$. |
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33 | %} |
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34 | %T. Marrodan Undagoitia 10/12/06 END Small corrections |
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35 | |
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36 | |
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37 | |
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38 | In fact approximately 67\% of the total reactor |
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39 | $\bar{\nu}_e$ flux at Fréjus originates from four nuclear power plants |
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40 | in the Rhone valley, located at distances between 115~km and 160~km. |
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41 | The indicated baselines are particularly suitable for |
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42 | the study of the $\bar{\nu}_e$ oscillations driven by $\Delta m_{21}^2$---they |
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43 | are similar to those exploited in the KamLAND experiment. |
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44 | % |
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45 | The authors of \cite{Petcov:2006gy} have investigated the possibility to use |
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46 | one module of MEMPHYS (147~kt fiducial mass) doped with Gadolinium (MEMPHYS-Gd) or the LENA detector, updating the previous work of \cite{Choubey:2004bf}. |
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47 | %T. Marrodan Undagoitia 10/12/06 START Small corrections |
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48 | %\REDBLA{ |
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49 | Above 3~MeV (2.6~MeV) the event rate is 59,980 (16,670) events/yr for |
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50 | MEMPHYS-Gd (LENA), which is 2 orders of magnitude larger than the |
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51 | KamLAND event rate. |
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52 | %} |
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53 | %T. Marrodan Undagoitia 10/12/06 END Small corrections |
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54 | |
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55 | |
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56 | \begin{figure} |
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57 | \includegraphics[width=\columnwidth]{./figures/LENAMEMPHYS-reac-histogram.eps} |
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58 | % |
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59 | \caption{The ratio of the event spectra in positron energy |
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60 | in the case of oscillations with $\Delta m_{21}^2 = 7.9\times 10^{-5}$~eV$^2$ and |
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61 | $\sin^2\theta_{12} = 0.30$ and in the absence of oscillations, |
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62 | determined using one year data of MEMPHYS-Gd and LENA located at Frejus. |
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63 | The error bars correspond to $1\sigma$ statistical error.} |
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64 | % |
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65 | \label{fig:LENAMEMPHYS-reac-histo} |
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66 | \end{figure} |
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67 | |
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68 | To test the sensitivity of the experiments the prompt energy |
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69 | spectrum is divided into 20 bins between 3~MeV |
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70 | and 12~MeV for MEMPHYS-Gd and SK-Gd, and into 25 bins between 2.6~MeV and |
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71 | 10~MeV for LENA (\refFig{fig:LENAMEMPHYS-reac-histo}). |
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72 | |
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73 | A $\chi^2$ analysis taking into account the statistical and systematical errors shows that each of the two |
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74 | detectors, MEMPHYS-Gd and LENA, if placed at Fréjus, would allow a |
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75 | very precise determination of the solar neutrino oscillation |
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76 | parameters $\Delta m_{21}^2$ and $\sin^2\theta_{12}$: with one year, the |
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77 | 3$\sigma$ uncertainties on $\Delta m_{21}^2$ and $\sin^2\theta_{12}$ can be |
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78 | reduced respectively to less than 3\% and to approximately 20\% (see also \refFig{fig:reactor-sensitivities}). In comparison, the |
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79 | Gadolinium doped Super-Kamiokande detector (SK-Gd) that might be envisaged in a near future can reach |
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80 | a similar precision if the SK/MEMPHYS fiducial mass ratio of 1 to 7 is |
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81 | compensated by a longer SK-Gd data taking time. |
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82 | % |
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83 | \begin{figure} |
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84 | \includegraphics[width=\columnwidth]{./figures/memphys-sk-sol-lena.eps} |
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85 | % |
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86 | \caption{The accuracy of the determination of $\Delta m_{21}^2$ and |
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87 | $\sin^2\theta_{12}$, which can be obtained using one year of data |
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88 | from MEMPHYS-Gd and LENA at Frejus, and from SK-Gd at Kamioka, |
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89 | compared to the current precision from solar neutrino and KamLAND |
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90 | data. We show the allowed regions at $3\sigma$ (2 d.o.f.) in the |
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91 | $\Delta m_{21}^2-\sin^2\theta_{12}$ plane, as well as the projections of the |
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92 | $\chi^2$ for each parameter.} |
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93 | % |
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94 | \label{fig:reactor-sensitivities} |
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95 | \end{figure} |
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96 | % |
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97 | Several years of reactor $\bar{\nu}_e$ data collected by |
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98 | MEMPHYS-Gd or LENA would allow a determination |
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99 | of $\Delta m_{21}^2$ and $\sin^2\theta_{12}$ with |
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100 | uncertainties of approximately 1\% and 10\% at 3$\sigma$, |
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101 | respectively. |
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102 | |
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103 | However, some caveat are worth to be mentioned. The prompt energy trigger of 3~MeV requires a very low PMT dark current rate in case of MEMPHYS detector. If the energy threshold is higher then the parameter precision decreases as can be seen on \refFig{fig:reactor-MEMPHYS-threshold} \cite{Schwetz:2006private}. The systematic uncertainties are also an important factor in the experiments under consideration, especially the determination of the |
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104 | mixing angle (eg. the energy scale and the overall normalization). |
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105 | % |
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106 | \begin{figure} |
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107 | \includegraphics[width=\columnwidth]{./figures/MEMPHYSGdreactorthreshold.eps} |
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108 | % |
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109 | \caption{The accuracy of the determination of $\Delta m_{21}^2$ and |
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110 | $\sin^2\theta_{12}$, which can be obtained using one year of data |
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111 | from MEMPHYS-Gd as a function of the prompt energy threshold.} |
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112 | % |
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113 | \label{fig:reactor-MEMPHYS-threshold} |
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114 | \end{figure} |
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115 | % |
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116 | Anyhow the accuracies on the solar oscillation parameters, which can be |
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117 | obtained in the high statistics experiments considered here are |
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118 | comparable to those that can be reached for the atmospheric neutrino |
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119 | oscillation parameters $\Delta m_{31}^2$ and $\sin^2\theta_{23}$ in future |
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120 | long-baseline superbeam experiments like T2HK in Japan or SPL from |
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121 | CERN to MEMPHYS. Hence, such reactor measurements would complete the |
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122 | program of the high precision determination of the leading neutrino |
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123 | oscillation parameters. |
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124 | %JEC 20/10/06 AND |
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125 | |
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126 | %It has been shown that using \WC\ loaded with Gadolinium to increase by a factor 10 the neutron capture one can expect 80\% (34\%) reduction of the spread of $\Delta m^2_{12}$ ($\theta_{12}$) in 110~kT.y exposure at Kamioka using SuperKamiokande. |
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127 | % |
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