Tests of Lorentz and $\mathit{CPT}$ symmetry with hadrons and nuclei

We explore the breaking of Lorentz and $\mathit{CPT}$ invariance in strong interactions at low energy in the framework of chiral perturbation theory. Starting from the set of Lorentz-violating operators of mass-dimension five with quark and gluon fields, we construct the effective chiral Lagrangian with hadronic and electromagnetic interactions induced by these operators. We develop the power-counting scheme and discuss loop diagrams and the one-pion-exchange nucleon-nucleon potential. The effective chiral Lagrangian is the basis for calculations of low-energy observables with hadronic degrees of freedom. As examples, we consider clock-comparison experiments with nuclei and spin-precession experiments with nucleons in storage rings. We derive strict limits on the dimension-five tensors that quantify Lorentz and $\mathit{CPT}$ violation.

Figure 1

Lorentz-violating contributions to the nucleon electromagnetic form factor. The square denotes the pion-nucleon vertex due to the Lorentz-violating tensor $D_{\mu \nu \rho }^{-}$, while the circles denote leading-order vertices from Eqs. (7) and (8).