Fate of the first-order chiral phase transition in QCD: Implications for dark QCD studied via a Nambu-Jona-Lasinio model

TL;DR

This paper investigates how weak external magnetic fields, possibly from early Universe magnetogenesis, can alter the first-order chiral phase transition in QCD-like theories, with implications for dark QCD and cosmological phenomena.

Contribution

It demonstrates that weak magnetic fields can eliminate the first-order nature of the chiral phase transition in QCD-like theories, challenging previous assumptions and impacting dark QCD models.

Findings

First-order transition disappears when magnetic field strength exceeds a critical value.

Magnetic catalysis and scale anomaly are key to the transition's behavior.

Results constrain models of dark QCD coupled to magnetic fields.

Abstract

The first-order nature of the chiral phase transition in QCD-like theories can play crucial roles to address a dark side of the Universe, where the created out-of equilibrium is essential to serve as cosmological and astrophysical probes such as gravitational wave productions, which have extensively been explored. This interdisciplinary physics is built based on a widely-accepted conjecture that the thermal chiral phase transition in QCD-like theories with massless (light) three flavors is of first order. We find that such a first order feature may not hold, when ordinary or dark quarks are externally coupled to a weak enough background field of photon or dark photon (which we collectively call a ``magnetic" field). We assume that a weak ``magnetic" background field could be originated from some ``magnetogenesis" in the early Universe. We work on a Nambu-Jona-Lasinio model which can describe the chiral phase transition in a wide class of QCD-like theories. We show that in the case with massless (light) three flavors, the first-order feature goes away when $2 f_\pi^2 \lesssim eB ( \ll (4 \pi f_\pi)^2)$, where $eB$ is the ``magnetic" field strength and $f_\pi$ the pion decay constant at the vacuum. This disappearance is the generic consequence of the presence of the ``magnetically" induced scale anomaly and the ``magnetic" catalysis for the chiral symmetry breaking, and would impact or constrain modeling dark QCD coupled to an external ``magnetic" field.