Corrections to the Gyromagnetic Factor in Very Special Relativity

Abstract

We consider Very Special Relativity corrections to the energy spectrum of a $C-$invariant Dirac Fermion in a static and homogeneous magnetic field $\vec B$. First, in the case of $\vec B$ parallel to the spatial VSR preferred direction $\vec n$, finding that the expression for the energy spectrum stays the same, except for a correction to the mass arising from the VSR contribution. Then, we relax the parallelism condition, finding a new equation for the energy spectrum. We solve this equation perturbatively. With a Penning trap's experiment in mind, we derive the first order VSR corrections to the electron's $g-2$ factor. Finally, using the current errors on the electron's $g$-factor measurements in Penning trap's experiments, we obtain an upper bound to the VSR electron mass parameter, and therefore also to the VSR electronic neutrino mass, of $0.824 \, eV$. This result does not contradict the possibility for VSR to be the origin of neutrino masses.