Baryon mass splittings and strong CP violation in SU(3) chiral perturbation theory

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 θ¯ 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 O(mq2). At lowest order, the CP-odd couplings induced by the QCD θ¯ term are determined by mass splittings of the baryon octet, the classic result of Crewther et al. [Phys. Lett. B 88, 123 (1979)PYLBAJ0370-269310.1016/0370-2693(79)90128-X]. We show that for each isospin-invariant CP-violating nucleon-meson interaction there exists one relation that 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 g¯0 by using recent lattice QCD evaluations of the proton-neutron mass splitting. In addition, we derive semiprecise values for CP-violating coupling constants between heavier mesons and nucleons with ∼30% uncertainty and discuss their phenomenological impact on electric dipole moments of nucleons and nuclei