QCD at Theta ~ Pi reexamined: domain walls and spontaneous CP violation

TL;DR

This paper reexamines QCD at Theta near Pi, revealing spontaneous CP violation, domain wall structures, and phase transitions, with detailed analysis across different flavor numbers and quark mass regimes.

Contribution

It provides a comprehensive analysis of QCD at Theta ~ Pi, including spontaneous CP violation, domain wall tensions, and phase transition structures using the effective Lagrangian approach.

Findings

CP is spontaneously broken at Theta=Pi for Nf=2 with mass splittings.

Line of first order transitions at Theta=Pi with critical endpoints in the z-Theta plane.

Domain wall tensions match chiral perturbation theory results for Mu=Md.

Abstract

We consider QCD at Theta ~ Pi with two, one and zero light flavours Nf, using the Di Vecchia-Veneziano-Witten effective lagrangian. For Nf=2, we show that CP is spontaneously broken at Theta = Pi for finite quark mass splittings, z= Md/Mu \not= 1. In the z-Theta plane, there is a line of first order transitions at Theta = Pi with two critical endpoints, z1* < z < z2*. We compute the tension of the domain walls relating the two CP violating vacua. For Mu=Md the tension of the family of equivalent domain walls agrees with the expression derived by Smilga from chiral perturbation theory at next-to-leading order. For z1* < z < z2*, z \not= 1, there is only one domain wall and a wall-some sphaleron at Theta = Pi. At the critical points, z = z*, the domain wall fades away, CP is restored and the transition becomes of second order. For Nf = 1, CP is spontaneously broken only if the number of colours Nc is large and/or if the quark is sufficiently heavy. Taking the heavy quark limit (~ Nf= 0) provides a simple derivation of the multibranch Theta dependence of the vacuum energy of large Nc pure Yang-Mills theory. In the large Nc limit, there are many quasi-stable vacua with decay rate Gamma ~ exp(-N_c^4).