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

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.