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 θ 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 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 θ 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 ∼20%, while for the isovector coupling, more substantial corrections are possible.
Additional Information© 2017 American Physical Society. Received 9 December 2016; revised manuscript received 24 October 2017; published 19 December 2017. We thank Barry Holstein, Emanuele Mereghetti, and Jordy de Vries for useful discussions. This work was supported in part under US Department of Energy Contract No. DE-SC0011095. C.Y.S. also acknowledges support by National Natural Science Foundation of China (NSFC) under Grants No. 11575110, No. 11655002, and No. 11735010, Natural Science Foundation of Shanghai under Grants No. 15DZ2272100 and No. 15ZR1423100, by the Shanghai Key Laboratory for Particle Physics and Cosmology, and by the Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education. He also appreciates the support through the Recruitment Program of Foreign Young Talents from the State Administration of Foreign Expert Affairs, China.
Published - PhysRevC.96.065204.pdf
Submitted - 1611.08063.pdf