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

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.

21 pages

References in corpus (6)

• Cerenkov Radiation in a Lorentz-Violating and Birefringent Vacuum
• Vacuum Cherenkov radiation for Lorentz-violating fermions
• Hadronic Lorentz Violation in Chiral Perturbation Theory
• Limits on Lorentz violation from charged-pion decay
• Gluonic Lorentz violation and chiral perturbation theory
• Test of Lorentz invariance in $\beta$ decay of polarized ${}^{20}\text{Na}$

Cited by in corpus (7)

• Gauge field theories with Lorentz-violating operators of arbitrary dimension
• The Lorentz- and CPT-Violating Standard Model Extension in Chiral Perturbation Theory
• Lorentz violation and the electron-ion collider
• $C$ and $CP$ violation in effective field theories
• Lorentz and CPT Violation in Partons
• Quark-sector Lorentz violation in $Z$-boson production
• A dimension five Lorentz-violating nonminimal coupling for mesons in the KLZ model