Abstract

We apply chiral-perturbation-theory techniques to the QCD sector of the Lorentz and CPT violating standard-model extension. We derive the effective Lagrangian in terms of pions and nucleons for a selected set of dimension-five operators involving quarks and gluons. This derivation is based on chiral-symmetry properties of the operators, as well as on their behaviour under C,P, and T transformations. We consider the power counting rules and apply the heavy-baryon approach to account for the large nucleon mass. Having obtained the relevant Lorentz-violating contributions to the pion-nucleon Lagrangian, we proceed to derive the particle and anti-particle Hamiltonian, from which we obtain the Lorentz-violating contribution to comagnetometer experiments. This allows us to place stringent limits on some of the parameters. For some other parameters we find that the best bounds will come from nucleon-nucleon interactions, and we derive the relevant nucleon-nucleon potential. These considerations imply possible new opportunities for spin-precession experiments involving for example the deuteron.

Highlights

  • Lorentz symmetry [1,2,3], the covariance of the laws of physics under rotations and boosts in four-dimensional spacetime, plays a central role in physics and is at the basis of the standard model (SM) of particle physics and general relativity

  • We explore the use of chiral perturbation theory, the low-energy EFT of quantum chromodynamics (QCD) [15, 16], to investigate the consequences of several higher-dimensional Lorentz violation (LV) operators with quark and gluon fields

  • The tensor in Eq (16a) is the simplest contribution to D F, with D F +,1 and D F −,1, together with LV low-energy constant (LEC) of order O(Fπ/Λχ). (Dν±ρσ contributes to both D F +,1 and D F +,1, due to isospin-breaking from the quark charges.) Eq (16b) is interesting because this operator gets a contribution from loop corrections due to the dominant D−-dependent πN interaction given in Eq (12), which is enhanced by a chiral logarithm, cf

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Summary

INTRODUCTION

Lorentz symmetry [1,2,3], the covariance of the laws of physics under rotations and boosts in four-dimensional spacetime, plays a central role in physics and is at the basis of the standard model (SM) of particle physics and general relativity. The tensors parametrize LV, which presumably originates from more fundamental Lorentz-tensor fields that obtained a vacuum expectation value through spontaneous symmetry breaking at high energy This approach has led to the standard-model extension (SME) [9], which is the most general and widely-used framework for theoretical and experimental considerations of Lorentz and CPT violation in particle physics. Most precision tests of Lorentz and CPT symmetry take place at low energies where quantum chromodynamics (QCD) is nonperturbative This complicates the study of LV operators that contain quark or gluon fields, to the extent that only a relatively small number of direct bounds exists for the strong sector [10]. Appendix B is devoted to the use of field redefinitions to reduce the number of effective operators

Operators with quarks and gluons
Operators with nucleons and pions
Heavy-baryon formalism
Pion-loop diagrams
Nucleon-nucleon interactions from one-pion exchange
HAMILTONIAN WITH LORENTZ VIOLATION
Clock-comparison experiments
Spin-precession experiments
Electromagnetic form factor
SUMMARY AND OUTLOOK
Findings
Naive dimensional analysis
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