Parity- and Time Reversal-Violating Pion Nucleon Couplings: Higher Order Chiral Matching Relations

Abstract

Parity- and time reversal-violating (PVTV) pion-nucleon couplings govern the magnitude of long-range contributions to nucleon and atomic electric dipole moments. When these couplings arise from chiral symmetry-breaking CP-violating operators, such as the QCD $\theta$-term or quark chromoelectric dipole moments, one may relate hadronic matrix elements entering the PVTV couplings to nucleon and pion mass shifts by exploiting the corresponding chiral transformation properties at leading order (LO) in the chiral expansion. We compute the higher-order contributions to the lowest order relations arising from chiral loops and next-to-next-to leading order (NNLO) operators. We find that for the QCD $\theta$-term the higher order contributions are analytic in the quark masses, while for the quark chromoelectric dipole moments and chiral symmetry-breaking four-quark operators, the matching relations also receive non-analytic corrections. Numerical estimates suggest that for the isoscalar PVTV pion-nucleon coupling, the higher order corrections may be as large as $\sim 20\%$, while for the isovector coupling, more substantial corrections are possible.

50 pages, 2 figures, 4 tables

References in corpus (12)

• An Improved Experimental Limit on the Electric Dipole Moment of the Neutron
• A Revised Experimental Upper Limit on the Electric Dipole Moment of the Neutron
• Reduced Limit on the Permanent Electric Dipole Moment of ${}^{199}$Hg
• Mesonic low-energy constants
• Unraveling models of CP violation through electric dipole moments of light nuclei
• Nucleon mass and sigma term from lattice QCD with two light fermion flavors
• Strong-Isospin Violation in the Neutron-Proton Mass Difference from Fully-Dynamical Lattice QCD and PQQCD
• An ${\epsilon }^{\prime }$ improvement from right-handed currents
• P- and T-Violating Lagrangians in Chiral Effective Field Theory and Nuclear Electric Dipole Moments
• The electric dipole moment of the deuteron from the QCD $\theta$-term
• Lattice QCD spectroscopy for hadronic CP violation
• Permanent Electric Dipole Moments of Single-, Two-, and Three-Nucleon Systems

Cited by in corpus (12)

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• Lattice QCD spectroscopy for hadronic CP violation
• A low-energy perspective on the minimal left-right symmetric model
• Relating hadronic CP-violation to higher-twist distributions
• Effective Field Theory in The Study of Long Range Nuclear Parity Violation on Lattice
• Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation
• Electric dipole moments of three-nucleon systems in the pionless effective field theory
• Electric dipole moments: a theory overview
• Strong CP Violation and large-$N_c$ spin-flavor symmetry