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.
Highlights
For the last two decades, there has been a renewed interest in the possibilities for the seemingly fundamental Lorentz and CPT symmetries to be violated in nature
Studies motivated by the first two reasons led to the development of a comprehensive effective field theory (EFT) describing LV physics, and it was found that there was a much richer array of possible forms that the Lorentz violation could take than had previously been realized
The most important product of this analysis is that we have derived definite forms for the LO couplings of pions and nucleons to external gauge fields. This provides a rigorous justification for the way proton Lorentz violation has been handled in many previous analyses, but it demonstrates that the conclusions of some existing work are not well justified
Summary
For the last two decades, there has been a renewed interest in the possibilities for the seemingly fundamental Lorentz and CPT symmetries to be violated in nature. Studies motivated by the first two reasons led to the development of a comprehensive effective field theory (EFT) describing LV physics, and it was found that there was a much richer array of possible forms that the Lorentz violation could take than had previously been realized. In the same way that the standard model is formed by including all local, renormalizable, gaugeinvariant, Lorentz-conserving (LC) operators that can be built out of those fields, the SME is likewise built up, but without the requirement that the terms of the Lagrange density be Lorentz scalars. Using chiral perturbation theory (χPT) [5,6,7] techniques, in [8] we described the construction of an effective Lagrangian at the hadronic level corresponding to the allowed LV modifications of the quark kinetic term in the mSME.
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