Nonminimal Lorentz invariance violation in light of the muon anomalous magnetic moment and long-baseline neutrino oscillation data

Abstract

In light of the increasing hints of new physics at the muon $g\ensuremath{-}2$ and neutrino oscillation experiments, we consider the recently observed tension in the long-baseline neutrino oscillation experiments as a potential indication of Lorentz invariance violation. For this purpose, the latest data from T2K and $\mathrm{NO}\ensuremath{\nu}\mathrm{A}$ is analyzed in the presence of nonminimal Lorentz invariance violation. Indeed, we find that isotropic violation in dimensions $D=4$, 5, and 6 can alleviate the tension in neutrino oscillation data by about $0.4--2.4\ensuremath{\sigma}$ confidence level significance, with the isotropic coefficient ${\ensuremath{\gamma}}_{\ensuremath{\tau}\ensuremath{\tau}}^{(5)}=3.58\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}32}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}1}$ yielding the best fit. At the same time, the anomalous muon $g\ensuremath{-}2$ result can be reproduced with an additional nonisotropic violation of ${d}^{zt}=\ensuremath{-}1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}$. The analysis highlights the possibility of simultaneous relaxation of experimental tensions with Lorentz invariance violation of a mixed nature.