Non-metricity effects on electron scattering in bumblebee gravity

TL;DR

This paper explores how non-metricity in bumblebee gravity affects electron scattering, revealing isotropic and anisotropic modifications to the Coulomb potential and deriving constraints from atomic physics experiments.

Contribution

It provides a detailed analysis of non-metricity effects on electron interactions in bumblebee gravity, including dispersion relations, potentials, and experimental bounds, which were not previously studied.

Findings

Timelike background yields a rescaled Coulomb potential.

Spacelike background causes anisotropic, quadrupolar potential modulation.

Atomic physics experiments constrain the Lorentz-violating parameters.

Abstract

We investigate non-metricity effects on electron scattering in metric-affine bumblebee gravity, where spontaneous Lorentz symmetry breaking is induced by a vector field acquiring a nonzero vacuum expectation value. Treating the affine connection as an independent variable and integrating it out leads to an effective description in which non-metricity modifies the dispersion relation of the bumblebee modes. From the full momentum-space propagator, we determine the pole structure that governs the interaction and construct the corresponding static Green function and interparticle potential. For a purely timelike background, the dispersion relation remains isotropic and produces a Coulomb potential with a uniformly rescaled effective coupling; consequently, the scattering amplitude preserves the Rutherford angular dependence, with the Lorentz-violating parameter entering only as an overall multiplicative factor. In contrast, a spacelike background induces anisotropy in the dispersion relation, leading to an orientation-dependent potential characterized by a quadrupolar modulation. This anisotropic structure propagates to the differential and integrated cross sections, introducing directional dependence while preserving the long-range character of the interaction. Finally, we consider phenomenological constraints from atomic physics. Hydrogen spectroscopy constrains the isotropic sector associated with the timelike configuration, whereas searches for anisotropies provide stronger limits on the quadrupolar contribution governed by $\xi b^{2}$.