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

Parity-violating 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 charge-parity-violating (CP-violating) operators, such as the QCD. term or quark chromoelectric dipole moments, one may relate hadronicmatrix elements entering thePVTVcouplings to nucleon and pionmass shifts by exploiting the corresponding chiral transformation properties at leading order 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 operators. We find that, for the QCD. 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 nonanalytic corrections. Numerical estimates suggest that, for the isoscalar PVTV pion-nucleon coupling, the higher order corrections may be as large as similar to 20%, while for the isovector coupling, more substantial corrections are possible.