Conformal Behavior in QCD

TL;DR

This paper explores the conformal behavior of quarks and gluons at finite temperature in QCD with 2 to 6 flavors, identifying an IR fixed point and analyzing meson correlation functions to understand phase transition properties.

Contribution

It introduces the existence of an IR fixed point at T > T_c in QCD and characterizes meson correlators with a power-law corrected Yukawa decay in the conformal region.

Findings

Correlation functions decay with a power-law corrected Yukawa form.

Identification of an IR fixed point at T > T_c.

Modification of chiral phase transition arguments.

Abstract

We give a new perspective on the properties of quarks and gluons at finite temperature T in N_f = 2 ~ 6 QCD. We point out the existence of an IR fixed point for the gauge coupling constant at T>T_c (T_c is the chiral phase transition temperature). Based on this observation we predict theoretically and verify numerically that the correlation functions of a meson G(t) at T/T_c > 1 decay with a power-law corrected Yukawa-type decaying form, G(t)=c exp(-m t)/t^alpha in the "conformal region" defined by m < c Lambda_IR, where Lambda_IR is the IR cutoff, m is the characteristic scale of the spectrum in the meson cannel and c is a constant of order 1. The decaying form is the characteristics of conformal theories with an IR cutoff. We discuss in detail how the resulting hyper scaling relation of physical observables may modify the existing argument about the order of the chiral phase transition in the N_f=2 case.