Chiral perturbation theory in a theta vacuum

TL;DR

This paper explores how a non-zero theta term affects chiral perturbation theory, revealing vacuum shifts, CP violation effects, and topology fixing impacts on mesonic correlators at one-loop order.

Contribution

It provides a detailed analysis of theta-dependent effects in ChPT, including vacuum structure, operator mixing, and topology fixing, up to second order in theta.

Findings

Vacuum shifts to non-trivial SU(N_f) elements

Mixing of CP eigenstates due to CP violation

Quantitative effects on mesonic correlators at one-loop

Abstract

We consider chiral perturbation theory (ChPT) with a non-zero theta term. Due to the CP violating term, the vacuum of chiral fields is shifted to a non-trivial element on the SU(N_f) group manifold. The CP violation also provides mixing of different CP eigenstates, between scalar and pseudoscalar, or vector and axialvector operators. We investigate upto O(theta^2) effects on the mesonic two point correlators of ChPT to the one-loop order. We also address the effects of fixing topology, by using saddle point integration in the Fourier transform with respect to theta.