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

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