Nucleon electric dipole moments and the isovector parity- and time-reversal-odd pion–nucleon coupling

The isovector time-reversal- and parity-violating pion–nucleon coupling g^¯_π⁽¹⁾ is uniquely sensitive to dimension-six interactions between right-handed light quarks and the Standard Model Higgs doublet that naturally arises in left-right symmetric models. Recent work has used the g^¯_π⁽¹⁾-induced one-loop contribution to the neutron electric dipole moment d_n, together with the present experimental d_n bound, to constrain the CP-violating parameters of the left-right symmetric model. We show that this and related analyses are based on an earlier meson theory d_n computation that is not consistent with the power-counting appropriate for an effective field theory. We repeat the one-loop calculation using heavy baryon chiral perturbation theory and find that the resulting d_n sensitivity to g^¯_π⁽¹⁾ is suppressed, implying more relaxed constraints on the parameter space of the left-right symmetric model. Assuming no cancellations between this loop contribution and other contributions, such as the leading order EDM low-energy constant, the present limit on d_n implies |g^¯_π⁽¹⁾|≲1.1×10⁻¹⁰