The Effective Chiral Lagrangian From Dimension-Six Parity and Time-Reversal Violation

TL;DR

This paper classifies dimension-six operators violating parity and time-reversal symmetry involving quarks and gluons, constructs the corresponding chiral Lagrangian, and applies it to calculate low-energy observables like nucleon EDMs.

Contribution

It provides a systematic classification of T- and P-violating operators and develops a power-counting scheme for deriving the effective chiral Lagrangian from these operators.

Findings

Constructed the effective chiral Lagrangian for P- and T-violating operators.

Calculated the parity- and time-reversal-violating pion-nucleon form factor.

Discussed implications for nucleon and light nuclei electric dipole moments.

Abstract

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.