Baryon mass splittings and strongCPviolation in SU(3) chiral perturbation theory

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 QCDθ 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(m 2 q ). At lowest order, the CP -odd couplings induced by the QCDθ 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 couplinḡ 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 ∼ 30% uncertainty and discuss their phenomenological impact on electric dipole moments of nucleons and nuclei.

Parity-violating and time-reversal-violating pion-nucleon couplings: Higher order chiral matching relations

“…[12,18,23] and references therein). The QCD Lagrangian with a nonzero θ term takes the following form:…”

“…For instance, Ref. [18] studied the higher-order effects to the matching formulas induced by a QCD θ term in a three-flavor ChPT. They found that, when the matching relation ofḡ (0) π is expressed in terms of the nucleon mass splitting, then its form is preserved by the chiral loop correction.…”

“…The latter may be obtained by lattice gauge theory or other phenomenological approaches. For example, application to the θ term with a lattice value of nucleon mass shift yields g (0) π ≈ (0.0155 ± 0.0025)θ [18]. (i) loop are evaluated at the renormalization scale μ = 1 GeV assuming all the nucleon mass shifts induced by non-quark-mass operators are zero.…”

“…[18] to cover all effective operators up to dimension six that include only the first generation quarks based on two-flavor heavy baryon chiral perturbation theory (HBChPT) in the SU(2) L × SU(2) R representation. First, we perform a general study of how these operators break chiral symmetry by using the spurion method.…”

Nucleon electric dipole moment with the gradient flow: Theθ-term contribution

“…As such, chiral symmetry relatesḡ θ 0 to known CP-even LECs [21,22]. In particular, it is possible to write [23] 9) where (M N − M P ) strong is the quark-mass induced part of the proton-neutron mass splitting,m = (…”