The effective chiral Lagrangian from the theta term

We construct the effective chiral Lagrangian involving hadronic and electromagnetic interactions originating from the QCD θ¯ term. We impose vacuum alignment at both quark and hadronic levels, including field redefinitions to eliminate pion tadpoles. We show that leading time-reversal-violating (TV) hadronic interactions are related to isospin-violating interactions that can in principle be determined from charge-symmetry-breaking experiments. We discuss the complications that arise from TV electromagnetic interactions. Some implications of the expected sizes of various pion–nucleon TV interactions are presented, and the pion–nucleon form factor is used as an example.