Consequences of neutrino Lorentz violation for leptonic meson decays

Abstract

If the observation by OPERA of apparently superluminal neutrinos is correct, the Lagrangian for second-generation leptons must break Lorentz invariance. We calculate the effects of an energy-independent change in the neutrino speed on another observable, the charged pion decay rate. The rate decreases by a factor $[1\ensuremath{-}\frac{3}{1\ensuremath{-}{m}_{\ensuremath{\mu}}^{2}/{m}_{\ensuremath{\pi}}^{2}}(⟨{v}_{\ensuremath{\nu}}⟩\ensuremath{-}1)]$, where $⟨{v}_{\ensuremath{\nu}}⟩$ is the (directionally averaged) neutrino speed in the pion's rest frame. This provides a completely independent experimental observable that is sensitive to the same forms of Lorentz violation as a neutrino time-of-flight measurement.