# Lorentz-violating nonminimal coupling contributions in mesonic hydrogen atoms and generation of photon higher-order derivative terms

## TL;DR

This paper investigates how Lorentz-violating nonminimal couplings affect mesonic hydrogen energy levels and photon sector corrections, setting upper bounds on these couplings through experimental data analysis.

## Contribution

It provides new upper bounds on CPT-odd and CPT-even Lorentz-violating couplings in mesonic hydrogen and explores higher-order photon derivative terms induced by these violations.

## Key findings

- CPT-odd coupling bound: <10^{-12} eV^{-1}
- CPT-even coupling bound: <10^{-16} eV^{-2}
- Identification of higher-order photon operators as dimension-5 and dimension-6 terms

## Abstract

We have studied the contributions of Lorentz-violating CPT-odd and CPT-even nonminimal couplings to the energy spectrum of the mesonic hydrogen and the higher-order radiative corrections to the effective action of the photon sector of a Lorentz-violating version of the scalar electrodynamics. By considering the complex scalar field describes charged mesons (pion or kaon), the non-relativistic limit of the model allows to attain upper-bounds by analyzing its contribution to the mesonic hydrogen energy. By using the experimental data for the $1S$ strong correction shift and the pure QED transitions $4P \rightarrow 3P$, the best upper-bound for the CPT-odd coupling is $<10^{-12}\text{eV}^{-1}$ and for the CPT-even one is $<10^{-16}\text{eV}^{-2}$. Besides, the CPT-odd radiative correction to the photon action is a dimension-5 operator which looks like a higher-order Carroll-Field-Jackiw term. The CPT-even radiative contribution to the photon effective action is a dimension-6 operator which would be a higher-order derivative version of the minimal CPT-even term of the standard model extension.