A Solution to the Strong CP Problem

TL;DR

This paper investigates whether the strong CP problem in QCD can be resolved without new symmetries by using lattice simulations, revealing phase transitions that suggest  is naturally tuned to zero in the continuum limit.

Contribution

The study provides lattice simulation evidence supporting the idea that the strong CP problem may be solved without introducing new particles or symmetries, through phase transition behavior in related models.

Findings

Phase transition in  from confining to deconfining phase at large 

Critical  approaches zero as lattice parameter increases

Preliminary results indicate similar behavior in 4D SU(2) Yang-Mills theory

Abstract

One may argue that QCD solves the strong CP problem by itself, without having to introduce new symmetries and particles. To test this idea, a lattice simulation is performed. The problem is investigated in the CP$^3$ model first. It is found that the model has a first order phase transition in $\theta$ from a confining phase at small $\theta$ to a deconfining phase at large $\theta$, and that the critical value of $\theta$ decreases towards zero as $\beta$ is taken to infinity. This suggests that $\theta$ is tuned to zero in the continuum limit. Preliminary studies of the SU(2) Yang-Mills theory in four dimensions show a phase transition in $\theta$ as well, so that it is quite likely that the strong CP problem in QCD is solved along the same line.