Scaling laws near the conformal window of many-flavor QCD

TL;DR

This paper establishes universal scaling laws for key physical quantities in many-flavor QCD near the conformal window, linking critical exponents to the gauge coupling's behavior at the infrared fixed point.

Contribution

It introduces a universal framework connecting scaling laws and critical exponents in many-flavor QCD near the conformal window, supported by nonperturbative calculations.

Findings

Critical exponents are interrelated and determined by the gauge coupling's critical exponent.

Scaling laws for temperature, condensate, and decay constant are derived.

Nonperturbative RG calculations support the theoretical predictions.

Abstract

We derive universal scaling laws for physical observables such as the critical temperature, the chiral condensate, and the pion decay constant as a function of the flavor number near the conformal window of many-flavor QCD in the chiral limit. We argue on general grounds that the associated critical exponents are all interrelated and can be determined from the critical exponent of the running gauge coupling at the Caswell-Banks-Zaks infrared fixed point. We illustrate our findings with the aid of nonperturbative functional Renormalization Group (RG) calculations and low-energy QCD models.