Nonrelativistic effective potential of the bumblebee model

TL;DR

This paper derives the nonrelativistic effective potential in the bumblebee model, revealing Lorentz-violating modifications to Coulomb potential and hydrogen atom energy levels in a weak gravity regime.

Contribution

It provides the explicit form of the Breit potential in the bumblebee model, including Lorentz-violating corrections up to second order in the coupling constant.

Findings

The potential exhibits 1/r asymptotics at lower order, indicating massless behavior.

Higher-order terms introduce anisotropic Lorentz-violating modifications.

LV corrections affect hydrogen atom energy levels.

Abstract

In this paper, we explicitly obtain the nonrelativistic Breit potential in the bumblebee model arising in the weak gravity limit of the metric-affine bumblebee gravity, coupled to the spinor matter. In this theory, in the lower (second) order in the small coupling constant $\xi$ (and the second order in the LV vector $\beta_{\mu}$) it demonstrates the $1/r$ asymptotics, which naturally corresponds to the massless character of the theory, while higher orders in $\xi$ yield anisotropic modifications of the Coulomb potential due to the Lorentz symmetry breaking. For the lower-order modification of the effective potential, we calculate LV corrections to energy levels of the hydrogen atom.