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In light of the increasing hints of new physics at the muon $g-2$ andneutrino oscillation experiments, we consider the recently observed tension inthe long-baseline neutrino oscillation experiments as a potential indication ofLorentz invariance violation. For this purpose, the latest data from T2K andNO$\nu$A is analysed in presence of non-minimal Lorentz invariance violation.Indeed, we find that isotropic violation in dimensions $D =$ 4, 5 and 6 canalleviate the tension in neutrino oscillation data by 0.4$-$2.4$\sigma$ CLsignificance, with the isotropic coefficient $\gamma^{(5)}_{\tau \tau} =$3.58$\times$10$^{-32}$GeV$^{-1}$ yielding the best fit. At the same time, theanomalous muon $g-2$ result can be reproduced with an additional non-isotropicviolation of $d^{zt} =$ -1.7$\times$10$^{-25}$. The analysis highlights thepossibility of simultaneous relaxation of experimental tensions with Lorentzinvariance violation of mixed nature.

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