The analogy of the Lorentz-violating fermion-gravity and fermion photon couplings

TL;DR

This paper explores the analogy between fermion-gravity and fermion-photon interactions under Lorentz violation, revealing anomalous matter-gravity couplings and deriving bounds on LV parameters through theoretical and experimental analysis.

Contribution

It introduces a novel approach to analyze Lorentz-violating fermion-gravity couplings using a curved Lense-Thirring metric, extending understanding beyond linear gravitational potentials.

Findings

Derived a LV non-relativistic Hamiltonian with spin-dependent operators.

Predicted anomalous spin precession and gravitational acceleration due to LV.

Provided rough bounds on LV parameters from spin gravity experiments.

Abstract

By adopting a methodology proposed by R.J. Adler \etl, we study the interesting analogy between the fermion-gravity and the fermion-electromagnetic interactions in the presence of the minimal Lorentz-violating (LV) fermion coefficients. The one-fermion matrix elements of gravitational interaction (OMEGI) are obtained with a prescribed Lense-Thirring (LT) metric assuming test particle assumption. Quite distinct from the extensively studied linear gravitational potential, the LT metric is an essentially curved metric, and thus reveals the anomalous LV matter-gravity couplings as a manifestation of the so-called gravito-magnetic effects, which go beyond the conventional equivalence principle predictions. By collecting all the spin-dependent operators from the OMEGI with some reasonable assumptions, we get a LV non-relativistic Hamiltonian, from which we derive the anomalous spin precession and gravitational acceleration due to LV. Combined these results with certain spin gravity experiments, we get some rough bounds on several LV parameters, such as $|3\vec{\tilde{H}}-2\vec{b}|\leq1.46\times10^{-5}\mathrm{eV}$, with some ad hoc assumptions.