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In this paper a scenario with the participation of the exotic scalar S,tensor T and pseudoscalar couplings of the right-handed neutrinos in additionto the standard vector V, axial A couplings of the left-handed neutrinos in thelow-energy $(\nu_{\mu}e^{-})$ and $(\nu_{e}e^{-})$ scattering processes isconsidered. Neutrinos are assumed to be massive Dirac fermions and to bepolarized. Both reactions are studied at the level of the four-fermion pointinteraction. The main goal is to show that the physical consequence of thepresence of the right-handed neutrinos is an appearance of the azimuthalasymmetry in the angular distribution of the recoil electrons caused by thenon-vanishing interference terms between the standard and exotic couplings,proportional to the transverse neutrino polarization vector. The upper limitson the expected effect of this asymmetry for the low-energy neutrinos $(E_{\nu}< 1 MeV)$ are found. We also show that if the neutrino helicity rotation$(\nu_{eL} \to \nu_{eR})$ in the solar magnetic field takes place, the similareffect of the azimuthal asymmetry of the recoil electrons scattered by thesolar neutrinos should be observed. This effect would also come from theinterference terms between the standard $(V, A)_{L}$ and exotic $(S, T, P)_{R}$couplings. New-type neutrino detectors with good angular resolution couldsearch for the azimuthal asymmetry in event number.Comment: EPJ C style, 14 pages, 5 eps figures; to appear in Eur. Phys. J

Right-handed Dirac neutrinos in ν e– scattering and azimuthal asymmetry in recoil electron event rates