Spin couplings as witnesses of Planck scale phenomenology

Abstract

Modified dispersion relations (MDRs) and noncommutative geometries are phenomenological models of Planck-scale corrections to relativistic kinematics, motivated by several approaches to quantum gravity. High-energy astrophysical observations, while commonly used to test such effects, are limited by significant systematic uncertainties. In contrast, low-energy, nonrelativistic experiments provide greater control, with precision serving as an amplifier for Planck-suppressed corrections. We derive corrections to Pauli's equation for nonrelativistic spin-1/2 particles in a magnetic field, incorporating general MDRs and noncommutative geometries. Applying our framework to k-Poincar\'e symmetries and minimal-length quantum mechanics, we identify Planck-scale corrections accessible in the nonrelativistic regime. Using the electron's anomalous magnetic moment, we constrain model parameters, pushing the k-Poincar\'e scale in the bi-crossproduct representation beyond $10^{10}$ GeV. These results highlight the complementarity of low-energy precision tests and astrophysical observation in probing quantum gravity phenomenology.