Flavor dependence of chiral symmetry breaking and the conformal window

TL;DR

This paper studies how the number of quark flavors affects chiral symmetry breaking in QCD, identifying a critical flavor number and analyzing the nature of the phase transition using Dyson-Schwinger equations.

Contribution

It provides a nonperturbative calculation of the critical flavor number for chiral symmetry restoration and characterizes the phase transition's critical exponents.

Findings

Critical flavor number $N_f^c=6.81$ for chiral symmetry restoration

Chiral condensate exhibits a second order phase transition with exponent ~0.53

Implications for the walking regime near the conformal window

Abstract

We investigate the phase structure of Quantum Chromodynamics (QCD) in the vacuum as a function of quark flavor number $N_f$ within the chiral limit. By self-consistently solving the coupled DSEs for the quark and gluon propagators in a minimal QCD scheme, we elucidate the nonperturbative dynamics governing dynamical chiral symmetry breaking. Our calculations determine a critical flavor number of $N_f^c=6.81$ which marks the chiral symmetry restoration of quarks. Further analysis reveals the critical exponents of the chiral condensate as $ -\langle\bar{\psi} {\psi}\rangle\sim |N_f-N_f^c|^{0.53(9)}$, characterized the second order feature of this phase transition of chiral symmetry. Additionally, we discuss the implications for the walking regime towards the conformal window at larger flavor.