Fierz-complete NJL model study II: towards the fixed-point and phase structure of hot and dense two-flavor QCD

Abstract

Nambu-Jona-Lasinio-type models are often employed as low-energy models for the theory of the strong interaction to analyze its phase structure at finite temperature and quark chemical potential. In particular at low temperature and large chemical potential, where the application of fully first-principles approaches is currently difficult at best, this class of models still plays a prominent role to guide our understanding of the dynamics of dense strong-interaction matter. In this work, we consider a Fierz-complete version of the Nambu-Jona-Lasinio model with two massless quark flavors and study its renormalization group flow and fixed-point structure at leading order of the derivative expansion of the effective action. Sum rules for the various four-quark couplings then allow us to monitor the strength of the breaking of the axial $U_{\mathrm{A}}(1)$ symmetry close to and above the phase boundary. We find that the dynamics in the ten-dimensional Fierz-complete space of four-quark couplings can only be reduced to a one-dimensional space associated with the scalar-pseudoscalar coupling in the strict large-$N_{\mathrm{c}}$ limit. Still, the interacting fixed point associated with this one-dimensional subspace appears to govern the dynamics at small quark chemical potential even beyond the large-$N_{\mathrm{c}}$ limit. At large chemical potential, corrections beyond the large-$N_{\mathrm{c}}$ limit become important and the dynamics is dominated by diquarks, favoring the formation of a chirally symmetric diquark condensate. In this regime, our study suggests that the phase boundary is shifted to higher temperatures when a Fierz-complete set of four-quark interactions is considered.

29 pages, 9 figures

References in corpus (12)

• Exact evolution equation for the effective potential
• Color superconductivity in dense quark matter
• Chiral symmetry breaking in continuum QCD
• Non-perturbative quark, gluon and meson correlators of unquenched QCD
• Two lectures on color superconductivity
• Chiral phase boundary of QCD at finite temperature
• Fluctuations in the quark-meson model for QCD with isospin chemical potential
• The QCD Phase Boundary from Quark-Gluon Dynamics
• On the Phase Structure of Many-Flavor QED${}_3$
• UV fixed-point structure of the three-dimensional Thirring model
• Fierz-complete NJL model study: fixed points and phase structure at finite temperature and density
• Bose-Einstein condensation and Silver Blaze property from the two-loop $\Phi$-derivable approximation

Cited by in corpus (24)

• The nonperturbative functional renormalization group and its applications
• The QCD phase structure at finite temperature and density
• Chiral phase structure and critical end point in QCD
• Symmetric nuclear matter from the strong interaction
• QCD at finite temperature and density within the fRG approach: An overview
• Fierz-complete NJL model study III: Emergence from quark-gluon dynamics
• Remarks on nuclear matter: how an ${\omega }_0$ condensate can spike the speed of sound, and a model of $Z(3)$ baryons
• DoFun 3.0: Functional equations in Mathematica
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Strangeness Neutrality and QCD Thermodynamics
• Renormalization Group Studies of Dense Relativistic Systems
• The Myriad Uses of Instantons
• From quarks and gluons to color superconductivity at supranuclear densities
• A curvature bound from gravitational catalysis in thermal backgrounds
• Four-quark scatterings in QCD I
• Speed of sound in dense strong-interaction matter
• Four-quark scatterings in QCD II
• Emergent Canonical Spin Tensor in the Chiral-Symmetric Hot QCD
• Fluctuation-induced higher-derivative couplings and infrared dynamics of the Quark-Meson-Diquark Model
• Role of the conserved charges in the chiral symmetry restoration phase transition
• Functional renormalization of QCD in $1+1$ dimensions: four-fermion interactions from quark-gluon dynamics
• Dynamical symmetry breaking in Georgi-Glashow chiral-gauge theories
• Functional renormalization group study of a four-fermion model with $CP$ violation
• QCD chiral phase diagram from weak functional renormalization group