[416] | 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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