First-order CP phase transition in two-flavor QCD at $\theta = \pi$ under electromagnetic scale anomaly via a Nambu-Jona-Lasinio description

TL;DR

This paper investigates how a weak magnetic field influences the nature of the CP phase transition at θ=π in two-flavor QCD, revealing that the transition becomes first order due to electromagnetic scale anomaly effects modeled via NJL.

Contribution

It introduces a NJL model with electromagnetic scale anomaly to show the magnetic field induces a first order CP phase transition at θ=π, highlighting the role of electromagnetic effects.

Findings

The CP phase transition at θ=π becomes first order under magnetic fields.

The transition strength increases with magnetic field intensity.

Electromagnetic scale anomaly creates a potential barrier leading to criticality.

Abstract

We discuss the thermal CP phase transition in QCD at $\theta=\pi$ under a weak magnetic field background, where the electromagnetic scale anomaly gets significant. To explicitize, we work on a two-flavor Nambu-Jona-Lasinio model at $\theta=\pi$ in the mean field approximation, including the electromagnetic-scale anomaly term. We find that the thermal CP phase transition becomes first order and the strength of the first order gets more prominent as the magnetic field increases. The associated potential barrier is thermally created by the electromagnetic scale anomaly and gives rise to criticality due to the induced potential of a non-perturbative form $\sim \frac{|eB|^3}{f_\pi} \frac{|P|}{P^2 + m_0^2}$, where $eB$ denotes the magnetic field strength; $P$ the CP order parameter, and $m_0$ the isospin-symmetric current-quark mass.