# The Lorentz- and CPT-Violating Standard Model Extension in Chiral Perturbation Theory

## TL;DR

This paper develops a chiral perturbation theory framework to relate Lorentz- and CPT-violating operators at the quark-gluon level to hadronic observables, enabling new bounds on symmetry violations in baryons.

## Contribution

It extends chiral perturbation theory to include Lorentz- and CPT-violating operators from the standard model extension, linking quark-level violations to hadronic measurements.

## Key findings

- Derived relations between baryon-level coefficients and quark/gluon operators.
- Mapped dimension-3 operators to hadronic observables without new low-energy constants.
- Established bounds on differences in Lorentz violation coefficients for baryons.

## Abstract

Lorentz and CPT violation in hadronic physics must be tied to symmetry violations at the underlying quark and gluon level. Chiral perturbation theory provides a method for translating novel operators that may appear in the Lagrange density for color-charged parton fields into equivalent forms for effective theories at the meson and baryon levels. We extend the application of this technique to the study of Lorentz-violating and potentially CPT-violating operators from the minimal standard model extension. For dimension-4 operators, there are nontrivial relations between the coefficients of baryon-level operators related to underlying quark and gluon operators with the same Lorentz structures. Moreover, in the mapping of the dimension-3 operators from the quark and gluon level to the hadron level (considered here for the first time), many of the hadronic observables contain no new low-energy coupling constants at all, which makes it possible to make direct translations of bounds derived using experiments on one kind of hadron into bounds in a completely different corner of the hadronic sector. A notable consequence of this is bounds (at $10^{-15}$-$10^{-20}$ GeV levels) on differences $a^{\mu}_{B}-a^{\mu}_{B'}$ of Lorentz and CPT violation coefficients for $SU(3)_{f}$ octet baryons that differ in their structure by the replacement of a single valance $d$ quark by a $s$ quark. Never before has there been any proposal for how these kinds of differences could be constrained.