T-odd correlation in muon neutrino elastic scattering on polarized proton target

In this paper, we analyze the elastic scattering of the muon neutrino (_νμ${\nu }_{\mu }$) beam on the polarized proton target (PPT) in a presence of induced couplings, and predict how the existence of relative phases between the complex vector (weak magnetism) and axial (induced pseudoscalar) form factors of the proton with left-chirality _νμ${\nu }_{\mu }$ affects the azimuthal dependence of the differential cross section. The neutrinos are assumed to be Dirac fermions with non-zero mass and CPT symmetry is conserved. We show that the azimuthal asymmetry of recoil protons depends on the neutrino mass, but contributions are very tiny (∼10⁻⁵$\sim {10}^{-5}$). Analysis of the differential cross section in the case of pure vector and axial couplings at zero _νμ${\nu }_{\mu }$ mass limit and zero momentum transfer shows that the T-violating phase _βVA${\beta }_{\mathit{VA}}$ generates the T-odd, P-even triple correlation and it could be detected by measuring the asymmetry between the (0,π)$(0,\pi )$ and (π,2π)$(\pi ,2\pi )$ angles. It should be clearly stressed that the considered T-odd observable is not a genuine CP-violating quantity as it can also be produced by the T-invariant contributions due to the final state interactions (FSI). Their magnitude must be precisely estimated and subtracted from the measured observable to extract information on the possible time reversal violation (TRV). We also indicate the possibility of using the PPT in the neutrino telescope.