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Neutrino-electron scattering

Reactors are well suited to study $\overline{\nu}_ee^-$ scattering. Both charged (CC) and neutral weak currents (NC) are involved. They are expected to interfere if the NC and CC final state neutrinos are identical, as assumed in the Standard Model . A measurement of the differential cross section allows, in principle, to determine the Weinberg angle $sin^{2}\theta_{W}$ and to observe the interference which is expected to be destructive for reasonable values of $sin^{2}\theta_{W}$. Practically however $\overline{\nu}_{e}e^{-}\rightarrow\overline{\nu}_{e}e^{-}$ only has a good sensitivity to both effects, while $\nu_{e}e^{-} \rightarrow \nu_{e}e^{-}$ essentially probes the interference. In addition, provided their magnetic moments are non vanishing, neutrinos will have electromagnetic interactions, making them scatter from a left handed active state, from the point of view of weak interaction, into a sterile right handed state. The cross-section is proportional to the effective magnetic moment
\begin{displaymath}\mu_{\nu} =\sqrt{\sum_{\ell}\vert\mu_{e\ell}\vert^{2}},\;\;\;\;\;\;(\ell=e,\;\mu,\;\tau\ldots)\end{displaymath}

with $\mu_{\ell,\ell'}$ the neutrino magnetic moment matrix. This matrix can either be Dirac like, in which case both static ( $\ell=\ell'$) and transition ( $\ell\neq \ell'$) moments may be non-zero, or Majorana like, in which case the transition moments only may be finite, the static moments being exactly zero. If large enough, the magnetic moment will affect the cross-section for all neutrino interactions, and cause neutrinos to precess in magnetic fields. In fact, neutrino magnetic moments of order 10-11-10-10 $\mu_B$ have been invoked as an alternative explanation to neutrino oscillations for the observed solar neutrino deficit . On the other hand, data on stellar cooling and supernova collapse, analysed in the frame of appropriate stellar models, give stringent uper limits. Beam dumps at intermediate energy accelerators produce $\nu_e$ with energies from 0 to 50 MeV. A measurements of $\nu_{e}e^{-} \rightarrow \nu_{e}e^{-}$ scattering has been performed at the LAMPF beam dump. In spite of a limited statistics the experiment showed that there was no room for a constructive interference, and confirmed the destructive interference. As expected the experiment did not give a precise value for the Weinberg angle. It produced however an upper limit for the magnetic moment of the $\nu_e$$\mu_{\nu}<1.08\cdot10^{-9}$. Reactors produce $\overline{\nu}_{e}$ with lower energies, ranging from 0 to 8 MeV. The UC Irvine group led by F. Reines built the first detector dedicated to the study of $\overline{\nu}_{e}$ scattering. It was operated successfully at the Savannah River Plant (SRP), observing the process for the first time.Vogel and Engel, using the presently best determination of the reactor spectrum and fixing $sin^{2}\theta_{W}$ to the presently accepted value, find that the measured rate is larger than the expected one. Taken literally this discrepancy points to a neutrino magnetic moment $\mu_{\nu}=(2-4)\cdot 10^{-10}$. More recently, a group from the Kurtchatov Institute in Moscow has also successfully observed $\overline{\nu}_ee^-$ scattering. The measured rate is compatible with expectations, obtained with $\sin\theta_W=0.23$, and leads to the limit $\mu_{\nu}<2.4\cdot 10^{-10}$ $\mu_B$ for the neutrino magnetic moment. It clearly appears important to improve by a large factor on these results, and clarify the situation. For these reason the MUNU collaboration has built a new detector. It is being installed at Bugey. The central component is a 1 m3 CF4 time projection chamber (TPC) operated at 5 bar, which serves as active target. With its imaging capability the detector should provide a clear signature for good events. Some 10 events per day are expected, with a threshold on the electron kinetic energy of 500 keV. The background can be determined from the observed rate of backward electrons. To reduce the background the detector is surrounded by a liquid scintillator veto and anti-Compton detector, and by various shielding layers. In addition it is made with radiochemically very clean materials. Thanks to the low threshold, the experiment should be sensitive to magnetic moments of order $2-3\cdot10^{-11}$ $\mu_B$, a factor 10 better than in previous experiments. In principle, it is also possible to measure the neutrino magnetic moment by studying neutrino-nucleus scattering at low energy. The cross-section is enhanced by a factor Z2 because of coherence. The recoil energy of the nucleus is however very small, and difficult to detect with standard techniques. Cryogenic detectors, which are presently being developed and used, for instance to search for double beta decay or dark matter, do have the required sensitivity. Simultaneous measurement of the phonons and the ionisation allows to distinguish nuclear recoil from electron-recoil, leading to a major background suppression. This may make this scheme attractive. Instead of nuclear reactors, one may consider using electron capture radioactive sources. Both the GALLEX and the SAGE collaborations have calibrated their solar neutrino detectors with 51Cr sources. The GALLEX source had an activity of $61.9 \pm 1.2$ PBq at the end of irradiation. There are two advantages in using a source: the neutrinos have well defined energies, and it is possible to approach the source very closely. Large detector masses are nevertheless required to study neutrino-electron scattering. 


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