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 $$\kappa $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>κ</mml:mi> </mml:math> -Poincaré 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 $$\kappa $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>κ</mml:mi> </mml:math> -Poincaré scale in the bi-crossproduct representation beyond $$10^{10} ~\text {GeV}.$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>10</mml:mn> </mml:msup> <mml:mspace/> <mml:mtext>GeV</mml:mtext> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> These results highlight the complementarity of low-energy precision tests and astrophysical observations in probing quantum gravity phenomenology.