νμe (ν¯μe)scattering to test gauge theories and search for right-handed neutrinos

The scattered electron in ${\nu }_{\mu L}e \left({\overline{\nu }}_{\mu L}e\right)$ elastic scattering has a simple angular distribution: $\frac{d\sigma }{d{\Omega }_{\mathrm{c}.\mathrm{m}.\mathrm{}}}=a{E_{\mathrm{tot}}}^2[1+\frac{1}{4}b{(1+cos\theta )}^2]$, where $\theta$ is the angle between initial and final electrons and $a$, $b$ are two positive constants. We note that the observation of a small number of events can shed some light on the magnitude of $b$ particularly and serve as a check for various gauge theories [similarly for $\nu p \left(\overline{\nu }p\right)$ scattering, when the momentum transfer is small]. In addition, deviations from this simple angular distribution, if observed experimentally in ${\nu }_{\mu }e \left({\overline{\nu }}_{\mu }e\right)$ scattering (for instance, a small peak in the backward direction), would be positive evidence for the existence of right-hand neutrinos.