Renormalization Group Flow and Equation of State of Quarks and Mesons

TL;DR

This paper derives and solves nonperturbative flow equations for a linear sigma model with quarks, revealing a second order phase transition at around 150 MeV and calculating the equation of state and critical exponents.

Contribution

It introduces a renormalization group approach with heat kernel regularization to study the quark-meson system at finite temperature, providing new insights into phase transitions and critical behavior.

Findings

Identifies a second order phase transition at T_c ≈ 150 MeV.

Links low-temperature four-dimensional theory to high-temperature three-dimensional theory.

Calculates the equation of state and universal critical exponents.

Abstract

Nonperturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavors are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective potential. We determine the initial values of the coupling constants in the effective potential at zero temperature. Solving the evolution equations with the same initial values at finite temperature in the chiral limit, we find a second order phase transition at T_c \approx 150 MeV. Due to the smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory. We calculate the equation of state in the chiral limit and for finite pion masses and determine universal critical exponents.