The Effective Chiral Lagrangian From the Theta Term

TL;DR

This paper develops an effective chiral Lagrangian incorporating QCD theta term effects, linking time-reversal violation to observable isospin-violating interactions and discussing electromagnetic complications.

Contribution

It introduces a method to construct the effective chiral Lagrangian from the QCD theta term, including vacuum alignment and field redefinitions, to analyze T-violating hadronic interactions.

Findings

Leading T-violating interactions relate to isospin violation.

Electromagnetic T-violation interactions present complications.

Implications for pion-nucleon T-violating interactions are discussed.

Abstract

We construct the effective chiral Lagrangian involving hadronic and electromagnetic interactions originating from the QCD theta 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.