Nonrelativistic effective potential of the bumblebee model

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 ξ (and the second order in the Lorentz-violating (LV) vector β μ ) it demonstrates the 1/ r asymptotics, which naturally corresponds to the massless character of the theory, while higher orders in ξ 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.