Lattice QCD spectroscopy for hadronic CP violation

TL;DR

This paper proposes a lattice QCD-based method to calculate CP-violating pion-nucleon couplings, reducing theoretical uncertainties in interpreting nuclear EDM experiments and advancing understanding of CP violation beyond the Standard Model.

Contribution

It introduces a novel strategy using chiral symmetry relations to compute CP-violating couplings via lattice QCD, bypassing direct and difficult calculations.

Findings

Chiral symmetry relations are reliable up to NNLO in chiral perturbation theory.

The method links difficult-to-calculate couplings to easier nucleon sigma terms and mass splittings.

Discussion provided on practical lattice QCD calculations and phenomenological implications.

Abstract

The interpretation of nuclear electric dipole moment (EDM) experiments is clouded by large theoretical uncertainties associated with nonperturbative matrix elements. In various beyond-the-Standard Model scenarios nuclear and diamagnetic atomic EDMs are expected to be dominated by CP-violating pion-nucleon interactions that arise from quark chromo-electric dipole moments. The corresponding CP-violating pion-nucleon coupling strengths are, however, poorly known. In this work we propose a strategy to calculate these couplings by using spectroscopic lattice QCD techniques. Instead of directly calculating the pion-nucleon coupling constants, a challenging task, we use chiral symmetry relations that link the pion-nucleon couplings to nucleon sigma terms and mass splittings that are significantly easier to calculate. In this work, we show that these relations are reliable up to next-to-next-to-leading order in the chiral expansion in both SU(2) and SU(3) chiral perturbation theory. We conclude with a brief discussion about practical details regarding the required lattice QCD calculations and the phenomenological impact of an improved understanding of CP-violating matrix elements.