Hadronic Lorentz Violation in Chiral Perturbation Theory

TL;DR

This paper derives effective theories for pions and nucleons incorporating Lorentz violation from quark-level operators, enabling new bounds on pion Lorentz violation based on nucleon data, with bounds reaching 10^{-23}.

Contribution

It establishes a theoretical link between quark-level Lorentz violation and hadron-level effects using chiral perturbation theory, providing the first bounds on pion Lorentz violation from nucleon observations.

Findings

Bounds on four pion Lorentz violation parameters at 10^{-23} level.

Effective Lagrangians for pions and nucleons with Lorentz-violating terms.

Demonstrates that hadron-level Lorentz violation can be constrained by nucleon data.

Abstract

Any possible Lorentz violation in the hadron sector must be tied to Lorentz violation at the underlying quark level. The relationships between the theories at these two levels are studied using chiral perturbation theory. Starting from a two-flavor quark theory that includes dimension-four Lorentz-violation operators, the effective Lagrangians are derived for both pions and nucleons, with novel terms appearing in both sectors. Since the Lorentz violation coefficients for nucleons and pions are all related to a single set of underlying quark coefficients, it is possible to place approximate bounds on pion Lorentz violation using only proton and neutron observations. The resulting bounds on four pion parameters are at the $10^{-23}$ level, representing improvements of ten orders of magnitude.