Corrections to the gyromagnetic factor in very special relativity

Abstract

We consider the corrections arising from the SIM(2) invariant realization of Very Special Relativity (VSR) to the energy spectrum of a C-invariant Dirac Fermion in a static and homogeneous magnetic field B. First, we analyze the case of B parallel to the spatial VSR preferred direction n, finding that the expression for the energy spectrum stays the same, except for a mass shift 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 most accurate 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 1 eV. This result does not contradict the possibility for VSR to be the origin of neutrino masses.