In this paper, we analyze the polarized muon decay at rest (PMDaR) and elastic neutrino-electron scattering (ENES) admitting the non-standard V+A interaction in addition to standard V-A interaction. Considerations are made for Dirac massive muon neutrino and electron antineutrino. Moreover, muon neutrinos are transversely polarized. It means that the outgoing muon-neutrino beam is a mixture of the left- and right-chirality muon neutrinos and has a fixed direction of transverse spin polarization with respect to production plane. We show that the angle-energy distribution of muon neutrinos contains the interference terms between the standard V-A and exotic V+A couplings, which are proportional to the transverse components of muon neutrino spin polarization. They do not vanish in a limit of massless neutrino and include the relative phases to test the CP violation. In consequence, it allows to calculate a neutrino flux and an expected event number in the ENES (detection process) both for the standard model prediction and the case of neutrino left-right mixture.
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