Bounds on Cubic Lorentz-Violating Terms in the Fermionic Dispersion Relation

Abstract

We study the recently proposed Lorentz-violating dispersion relation for fermions and show that it leads to two distinct cubic operators in the momentum. We compute the leading order terms that modify the non-relativistic equations of motion and use experimental results for the hyperfine transition in the ground state of the ${}^9\text{B}{e}^{+}$ ion to bound the values of the Lorentz-violating parameters ${\eta }_1$ and ${\eta }_2$ for neutrons. The resulting bounds depend on the value of the Lorenz-violating background four-vector in the laboratory frame.

Revtex 4, four pages. Version to match the one to appear in Physical Review D