Novel Studies on the \eta' Effective Lagrangian

TL;DR

This paper revisits the ta' effective Lagrangian, performs its canonical quantization, and uncovers a new P- and T-violating chiral coupling involving fermions, with implications for electric dipole moments.

Contribution

It introduces a novel chirally symmetric, P- and T-violating coupling of the ta' field to fermions, expanding the understanding of its interactions.

Findings

Discovered a new ta'-fermion coupling that violates P and T symmetries.

Developed a canonical quantization framework considering topology and constraints.

Set the stage for future calculations of fermion electric dipole moments.

Abstract

The effective Lagrangian for \eta' incorporating the effect of the QCD \theta-angle has been developed previously. We revisit this Lagrangian and carry out its canonical quantization with particular attention to the test function spaces of constraints and the topology of the \eta'-field. In this way, we discover a new chirally symmetric coupling of this field to chiral multiplets which involves in particular fermions. This coupling violates P and T symmetries. In a subsequent paper, we will evaluate its contribution to the electric dipole moment (EDM) of fermions. Our motivation is to test whether the use of mixed states restores P and T invariance, so that EDM vanishes. This calculation will be shown to have striking new physical consequences.