QCD chiral phase diagram from weak functional renormalization group

TL;DR

This work applies a weak form of the functional renormalization group to QCD at finite $T$ and $\mu_B$, focusing on the purely fermionic sector and a scalar fermionic potential $V_k(\sigma;t)$ within the local potential approximation. By solving the resulting first-order PDEs for $V_k$ (via its mass function $M=\partial_\sigma V$) with the method of characteristics and a Rankine–Hugoniot condition, the authors extract the dynamical quark mass and map the chiral phase diagram in the $(\mu_B,T)$ plane. They compare ladder and beyond-ladder (non-ladder) truncations and investigate the impact of the quark anomalous dimension $\eta_\psi$, finding that non-ladder effects and HTL-inspired gluon dynamics yield $T_c(0)$ values in line with other continuum approaches, while the chiral critical behavior shows sizable deviations due to the truncation. The results illustrate that mesonic fluctuations play a subleading role near zero chemical potential but are necessary to realize realistic chiral criticality, highlighting the strengths and limitations of a fermion-only weak fRG framework for QCD phase structure.

Abstract

We investigate the QCD chiral phase transition at finite temperature and finite baryon density using the functional Renormalization Group (fRG). While conventional fRG studies often employ techniques such as dynamical bosonization to regularize divergences, we instead pursue the weak solution of the fRG equations which allows for non-analytic behavior in the flow to compute the pure fermionic potential $V_k(ψ,\barψ)$ within the local potential approximation. This approach enables us to explore the effects of purely quark-level fluctuations on dynamical chiral symmetry breaking without introducing any auxiliary bosonic fields. Based on this framework, we present the resulting chiral phase diagram as a function of temperature and baryon chemical potential.

Figures (11)

• Figure 1: QCD phase diagrams in terms of the phase boundary ($T_c$-lines) of second-order (chiral limit) or crossover (physical point) within the parameter setups in \ref{['tab:parameterFixing']}. The positions of the critical end point (CEP) in each case are marked by triangle markers.
• Figure 2: Sketch of the mixed quark-gluon vertex $\mathcal{A} + \mathcal{B}$. The solid line represents a fermion, while the curly lines correspond to gluons.
• Figure 3: Sketch of $(\mathcal{A}+\mathcal{B})^2 \to \mathcal{A}^2+ \mathcal{B}^2$ under the ladder approximation \ref{['eq:ladderAproxMainText']}.
• Figure 4: Example of diagrams that are not included in the "ladder" approximation scheme.
• Figure 5: Feynman diagram which contributes to the running gauge coupling induced from the 4-fermion interaction.