Elastic neutrino-atom scattering as a probe of neutrino millicharge and magnetic moment

Neutrino scattering on atomic systems at low-energy transfer is a powerful tool for searching the neutrino electromagnetic interactions. The regime of coherent elastic neutrino-atom scattering, i.e., when the atom recoils as a pointlike particle, can be effectively fulfilled in the case of tritium antineutrinos. We present theoretical calculations for coherent elastic neutrino-atom scattering processes on such targets as the H, $^2$H, $^3$He, and $^4$He %, and $^{12}$C atoms. We show how the atomic effects and neutrino electromagnetic properties, namely the neutrino millicharge and magnetic moment, may manifest themselves in the atomic-recoil spectra. Our results can be used in planning the experiments on coherent elastic neutrino-atom scattering (in particular, with superfluid He-4).


Introduction
The search for light particles of dark matter requires the detectors that are sensitive to low recoil energies ( 100 meV).This can be achieved, for example, by using a superfluid He-4 target [1].Another possible application of the superfluid He-4 detector could be the study of the low-energy neutrino scattering, in particular of the coherent elastic neutrino-atom scattering (CEAS) [2][3][4][5] that has not been observed so far.Below we inspect the sensitivity of the CEAS processes on light atomic systems to such neutrino electromagnetic properties as millicharge   and magnetic moment   [6].For this purpose we account for the indicated neutrino properties in the CEAS cross section and present the corresponding numerical results.

Effects of neutrino millicharge and magnetic moment in CEvAS
We consider an elastic neutrino-atom collision in the following kinematical regime: where   is the neutrino energy,  is the energy transfer,  is the atomic mass, and  nuc is the nuclear radius.
According to [2][3][4][7][8][9], the CEAS differential cross section is given by Here the weak interaction and neutrino millicharge contribution is with where  is the momentum transfer, with  2 = 2, the plus (minus) stands for  =   ( =  ,  ), and  () is the number of protons (neutrons) in the atomic nucleus. el ( 2 ) is the Fourier transform of the electron density,   = 1.25,  ± and  ± are the numbers of protons and neutrons (electrons) with spin parallel (+) or antiparallel (−) to the nucleus spin (the total electron spin).  ± is the number of electrons in the  atomic orbital with spin parallel (+) or antiparallel (−) to the electron spin, and   el ( 2 ) is the Fourier transform of the  electron density.The neutrino millicharge   is in units of .

Helium-4
CEνAS (e ν =0) CEνAS (e ν =-10 -15 e) CEνAS (e ν =+10 -15 e) where the neutrino magnetic moment   is in units of   .In contrast to the case of neutrino millicharge, the neutrino magnetic moment interaction flips the neutrino helicity, and therefore it does not interfere with the weak interaction channel.In Fig. 1 we present the numerical results for the differential cross section (1) in the case of an electron antineutrino with   = 10 keV that is typical for the tritium neutrino source.It can be seen that the atomic recoil spectra in CEAS processes on the H, 2 H, 3 He, and 4 He atomic systems are very sensitive to the neutrino millicharge and magnetic moment.Measuring these spectra may allow us to test the   and   values at a level of 10 −15  and 10 −12   , respectively, or even below that level.
The obtained results will be used in the search for the electromagnetic properties of neutrinos in the experiment involving an intense tritium neutrino source and a superfluid 4 He target.This experiment is currently being prepared in the framework of the research program of the National Center for Physics and Mathematics in Sarov, Russia.