Baryon mass splittings and strong CP violation in SU(3) Chiral Perturbation Theory

TL;DR

This paper uses SU(3) chiral perturbation theory up to NNLO to analyze baryon mass splittings and CP violation, deriving relations that help determine CP-violating couplings relevant for electric dipole moments.

Contribution

It provides the first next-to-next-to-leading order analysis of baryon mass splittings and CP-violating interactions, establishing relations that remain valid at this order.

Findings

Derived a precise value for the pion-nucleon coupling  g_0 using lattice QCD data.

Identified relations between CP-violating couplings that hold up to NNLO.

Estimated CP-violating couplings for heavier mesons with ~30% uncertainty.

Abstract

We study $SU(3)$ flavor-breaking corrections to the relation between the octet baryon masses and the nucleon-meson CP-violating interactions induced by the QCD $\bar\theta$ term. We work within the framework of $SU(3)$ chiral perturbation theory and work through next-to-next-to-leading order in the $SU(3)$ chiral expansion, which is $\mathcal{O}(m_q^2)$. At lowest order, the CP-odd couplings induced by the QCD $\bar\theta$ term are determined by mass splittings of the baryon octet, the classic result of Crewther et al. We show that for each isospin-invariant CP-violating nucleon-meson interaction there exists one relation which is respected by loop corrections up to the order we work, while other leading-order relations are violated. With these relations we extract a precise value of the pion-nucleon coupling $\bar g_0$ by using recent lattice QCD evaluations of the proton-neutron mass splitting. In addition, we derive semi-precise values for CP-violating coupling constants between heavier mesons and nucleons with $\sim 30\%$ uncertainty and discuss their phenomenological impact on electric dipole moments of nucleons and nuclei.