QCD phase transitions in the light quark chiral limit

TL;DR

This study investigates the nature of the QCD chiral transition in the light quark mass limit using an extended lattice and Dyson-Schwinger approach, finding a consistent second-order transition with no first-order region in the studied parameter space.

Contribution

First comprehensive analysis of the QCD chiral transition in a full (2+1)-flavor setup combining lattice Yang-Mills theory and Dyson-Schwinger equations.

Findings

Second-order phase transition throughout the studied range.

No evidence of a first-order region in the $N_{f} = 3$ corner of the Columbia plot.

Results consistent with lattice and functional renormalization group studies.

Abstract

We investigate the order of the QCD chiral transition in the limit of vanishing bare up/down quark masses and variations of the bare strange-quark mass $0 \le m_{\mathrm{s}} \le \infty$. In this limit and due to universality long range correlations with the quantum numbers of pseudoscalar and scalar mesons may dominate the physics. In order to study the interplay between the microscopic quark and gluon degrees of freedom and the long range correlations we extend a combination of lattice Yang--Mills theory and a (truncated) version of Dyson--Schwinger equations by also taking back-reactions of mesonic degrees of freedom into account. Both this system and the meson backcoupling approach have been studied extensively in the past but this is the first work in a full $(2 + 1)$-flavor setup. Starting from the physical point, we determine the chiral susceptibilities for decreasing up/down quark masses and find good agreement with both lattice and functional renormalization group results. We then proceed to determine the order of the chiral transition along the left-hand side of the Columbia plot, for chemical potentials in the range $-(30 \,\textrm{MeV})^2 \le \mu_q^2 \le (30 \,\textrm{MeV})^2$. We find a second-order phase transition throughout and no trace of a first-order region in the $N_{f} = 3$ corner of the Columbia plot. This result remains unchanged when an additional Goldstone boson due to a restored axial $\mathrm{U_A}(1)$ is taken into account.