Potentialities of a low-energy detector based on $^4$He evaporation to observe atomic effects in coherent neutrino scattering and physics perspectives

We propose an experimental setup to observe coherent elastic neutrino-atom scattering (CE$ν$AS) using electron antineutrinos from tritium decay and a liquid helium target. In this scattering process with the whole atom, that has not beeen observed so far, the electrons tend to screen the weak charge of the nucleus as seen by the electron antineutrino probe. The interference between the nucleus and the electron cloud produces a sharp dip in the recoil spectrum at atomic recoil energies of about 9 meV, reducing sizeably the number of expected events with respect to the coherent elastic neutrino-nucleus scattering case. We estimate that with a 60 g tritium source surrounded by 500 kg of liquid helium in a cylindrical tank, one could observe the existence of CE$ν$AS processes at 3$σ$ in 5 years of data taking. Keeping the same amount of helium and the same data-taking period, we test the sensitivity to the Weinberg angle and a possible neutrino magnetic moment for three different scenarios: 60 g, 160 g, and 500 g of tritium. In the latter scenario, the Standard Model (SM) value of the Weinberg angle can be measured with a statistical uncertainty of $\sin^2{\vartheta_W^{\mathrm{SM}}}^{+0.015}_{-0.016}$. This would represent the lowest-energy measurement of $\sin^2{\vartheta_W}$, with the advantage of being not affected by the uncertainties on the neutron form factor of the nucleus as the current lowest-energy determination. Finally, we study the sensitivity of this apparatus to a possible electron neutrino magnetic moment and we find that using 60 g of tritium it is possible to set an upper limit of about $7\times10^{-13}\,μ_B$ at 90% C.L., that is more than one order of magnitude smaller than the current experimental limit.