Towards a Dynamical Solution of the Strong CP Problem

TL;DR

This paper explores whether QCD can inherently resolve the strong CP problem, using lattice simulations of the $CP^3$ model as a simplified test case to observe phase transition behaviors related to the CP-violating parameter.

Contribution

It introduces a lattice simulation approach in the $CP^3$ model to investigate the potential self-resolution of the strong CP problem in QCD.

Findings

The $CP^3$ model exhibits a first-order deconfining phase transition in $ heta$.

The critical $ heta$ value decreases towards zero as $eta$ increases.

Results suggest $ heta$ is naturally tuned to zero in the continuum limit.

Abstract

It is argued that QCD might solve the strong CP problem on its own. To test this idea, a lattice simulation suggests itself. In view of the difficulty of such a calculation we have, as a first step, investigated the problem in the $CP^3$ model. The $CP^3$ model is in many respects similar to QCD. In this talk I shall present some first results of our calculation. Among other things it is shown that the model has a first order deconfining phase transition in $\theta$ 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.