Hadronic Lorentz Violation in Chiral Perturbation Theory Including the Coupling to External Fields

TL;DR

This paper develops a chiral perturbation theory framework to connect Lorentz violation at the quark level with observable effects in hadronic and electromagnetic processes, highlighting how certain experimental constraints relate to underlying quark coefficients.

Contribution

It derives a low-energy effective theory of pions and nucleons incorporating Lorentz violation, linking quark-level coefficients to hadronic and electromagnetic observables.

Findings

Electromagnetic couplings depend on specific quark coefficient combinations.

Observations of hadronic electromagnetic processes can constrain certain Lorentz-violating parameters.

The theory maintains local chiral invariance despite Lorentz violation.

Abstract

If any violation of Lorentz symmetry exists in the hadron sector, its ultimate origins must lie at the quark level. We continue the analysis of how the theories at these two levels are connected, using chiral perturbation theory. Considering a two-flavor quark theory, with dimension-4 operators that break Lorentz symmetry, we derive a low-energy theory of pions and nucleons that is invariant under local chiral transformations and includes the coupling to external fields. The pure meson and baryon sectors, as well as the couplings between them and the couplings to external electromagnetic and weak gauge fields, contain forms of Lorentz violation which depend on linear combinations of quark-level coefficients. In particular, at leading order the electromagnetic couplings depend on the very same combinations as appear in the free particle propagators. This means that observations of electromagnetic processes involving hadrons--such as vacuum Cerenkov radiation, which may be allowed in Lorentz-violating theories--can only reliably constrain certain particular combinations of quark coefficients.