Renormalization Group Flow and Equation of State of Quarks and Mesons

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.

35 pages, LaTeX, 18 eps-figures, subm. to Nucl. Phys. A

References in corpus (9)

• Exact evolution equation for the effective potential
• Two flavor chiral phase transition from nonperturbative flow equations
• Derivative expansion of the renormalization group in O(N) scalar field theory
• Pion Dynamics at Finite Temperature
• Rapidly Converging Truncation Scheme of the Exact Renormalization Group
• Nonperturbative γ^* p Interaction in the Diffractive Regime
• Application of the Heat Kernel Method to the Constituent Quark Model at Finite Temperature
• Scheme Independence of Blocking Transformation in Finite-Temperature Renormalization Group
• Thermodynamics of Constituent Quarks

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