On possibility of time reversal symmetry violation in neutrino elastic scattering on polarized electron target

Abstract

In this paper, we indicate a possibility of utilizing the elastic scattering of the Dirac low energy ($\sim 1$ MeV) electron neutrinos ($ν_e$'s) on the polarized electron target (PET) in testing the time reversal symmetry violation (TRSV). We consider a scenario in which the incoming $ν_e$ beam is the superposition of left chiral (LC) and right chiral (RC) states. LC $ν_e$'s interact mainly by the standard $V - A$, while RC ones are only detected by the exotic $V + A$ and $S_R, P_R, T_R$ interactions. One assumes that the spin polarization vector of the initial $ν_e$'s is turned aside from the $ν_e$ momentum, and due to this the non-vanishing transversal component of the $ν_e$ spin polarization appears. We compute the differential cross section as a function of the recoil electron azimuthal angle and scattered electron energy, and show how the interference terms between standard $V-A$ and exotic $S_R, P_R, T_R$ couplings depend on the various angular correlations among the transversal $ν_e$ spin polarization, the polarization of the electron target, the incoming neutrino momentum and the outgoing electron momentum in the limit of relativistic $ν_e$. We illustrate how the maximal value of recoil electrons azimuthal asymmetry and the asymmetry axis location of outgoing electrons depend on the azimuthal angle of the transversal component of the $ν_e$ spin polarization, both for the time reversal symmetry conservation (TRSC) and TRSV. Next, we display that the electron energy spectrum and polar angle distribution of the recoil electrons are also sensitive to the interference terms between $V - A$ and $S_R, P_R, T_R$ couplings, proportional to the T-even and T-odd angular correlations. Our model-independent analysis is carried out for the flavor $ν_e$'s.