The effective chiral Lagrangian from dimension-six parity and time-reversal violation

•Classification of TT-odd dimension-six sources based on impact on observables.•Building of the chiral Lagrangian for each dimension-six source.•Calculation of the PT-odd pion–nucleon form factor for each source.•Discussion of hadronic EDMs for each source and comparison with the theta term.

We classify the parity- and time-reversal-violating operators involving quark and gluon fields that have effective dimension six: the quark electric dipole moment, the quark and gluon chromo-electric dipole moments, and four four-quark operators. We construct the effective chiral Lagrangian with hadronic and electromagnetic interactions that originate from them, which serves as the basis for calculations of low-energy observables. The form of the effective interactions depends on the chiral properties of these operators. We develop a power-counting scheme and calculate within this scheme, as an example, the parity- and time-reversal-violating pion–nucleon form factor. We also discuss the electric dipole moments of the nucleon and light nuclei.