Scattering of neutrinos on a polarized electron target as a test for new physics beyond the standard model

Abstract

In this paper, we analyze the scattering of the neutrino beam on the polarized electron target, and predict the effects of two theoretically possible scenarios beyond the standard model. In both scenarios, our results are presented in a massless neutrino limit. First, we consider how the existence of $CP$ violation phase between the complex vector $V$ and axial $A$ couplings of the left-handed neutrinos affects the azimuthal dependence of the differential cross section. The azimuthal angle ${\ensuremath{\phi}}_{{e}^{\ensuremath{'}}}$ of outgoing electron momentum is measured with respect to the transverse component of the initial electron polarization ${\mathbit{\ensuremath{\eta}}}_{\mathbit{e}}^{\ensuremath{\perp}}$. We indicate the possibility of using the polarized electron target to measure the $CP$ violation in the ${\ensuremath{\nu}}_{\ensuremath{\mu}}{e}^{\ensuremath{-}}$ scattering. The future superbeam and neutrino factory experiments will provide the unique opportunity for the leptonic $CP$ violation studies, if the large magnetized sampling calorimeters with good event reconstruction capabilities are build. Next, we take into account a scenario with the participation of the exotic complex scalar $S$ coupling of the right-handed neutrinos in addition to the standard real vector $V$ and axial $A$ couplings of the left-handed neutrinos. The main goal is to show how the presence of the $R$-handed neutrinos, in the above process changes the spectrum of recoil electrons in relation to the expected standard model prediction, using the current limits on the nonstandard couplings. The interference terms between the standard and exotic couplings in the differential cross section depend on the angle $\ensuremath{\alpha}$ between the transverse incoming neutrino polarization and the transverse electron polarization of the target. The detection of the dependence on this angle in the energy spectrum of recoil electrons would be a signature of the presence of the $R$-handed neutrinos in the neutrino-electron scattering. To make this test feasible, the polarized artificial neutrino source needs to be identified.