Upper limit on the magnetic moment of the neutrino

Abstract

We have recalculated the processes $e\ensuremath{\nu}\ensuremath{\rightarrow}e\ensuremath{\nu}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ due to an assumed magnetic moment $\ensuremath{\kappa}$ of the neutrino (correcting some errors in the previous calculations). Comparing the results with the Fermi and electroweak models we set a suggestive limit $\ensuremath{\kappa}\ensuremath{\lesssim}{(\frac{\mathrm{gm}}{e{M}_{Z}})}^{2}{\ensuremath{\mu}}_{0}$, where $m$ is the electron mass and ${\ensuremath{\mu}}_{0}=\frac{e}{2m}$. A very sensitive method to set a good upper limit would be to measure the angular distribution of $e\ensuremath{\nu}\ensuremath{\rightarrow}e\ensuremath{\nu}$ near the forward direction.