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arXiv · 2512.17507

Nonrelativistic effective potential of the bumblebee model

C. Furtado·J. R. Nascimento·A. Yu. Petrov·P. Porfirio
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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.

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C. Furtado, J. R. Nascimento, A. Yu. Petrov, P. Porfirio. 2025-12-19. Nonrelativistic effective potential of the bumblebee model. https://doi.org/10.1016/j.nuclphysb.2026.117540

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