Planck-Scale Signatures in Vacuum Neutrino Oscillations

Abstract

We present a closed-form perturbative framework for two-flavour vacuum neutrino oscillations in the presence of a weak, flavour-blind Planck-scale mass correction generated by the dimension-five Weinberg operator of the Standard Model Effective Field Theory. The perturbative treatment is developed in direct structural analogy with approaches used to describe weak Earth-matter effects. We derive simple analytical expressions for the modification of the oscillation length, the oscillation phase, and the flavour-conversion probability, valid for arbitrary neutrino mixing and baseline lengths. Unlike matter-induced perturbations, the Planck-scale correction is constant along the neutrino trajectory. Consequently, its effect on the transition probability remains bounded and independent of the baseline at the amplitude level, while the associated modification of the effective mass-squared splitting produces a phase mismatch that increases linearly with propagation distance. We further present illustrative order-of-magnitude sensitivity projections for next-generation long-baseline and reactor neutrino experiments, including DUNE, Hyper-Kamiokande, and JUNO. Our results indicate that the accumulated phase drift provides a particularly promising observable for probing Planck-scale mass corrections and for distinguishing a possible quantum-gravity contribution from conventional matter-induced effects.