The Quark-Mass Dependence of T_C in QCD: Working up from m=0 or down from m=infinity ?

Abstract

We analyze the dependence of the QCD transition temperature on the quark (or pion) mass. We find that a linear sigma model, which links the transition to chiral symmetry restoration, predicts a much stronger dependence of T_c on m_pi than seen in present lattice data for m_pi >~ 0.4 GeV. On the other hand, working down from m_pi=infinity, an effective Lagrangian for the Polyakov loop requires only small explicit symmetry breaking, b_1 ~ exp(-m_pi), to describe T_c(m_pi) in the above mass range. Physically, this is a consequence of the flat potential (large correlation length) for the Polyakov loop in the three-color pure gauge theory at T_c. We quantitatively estimate the end point of the line of first order deconfining phase transitions: m_pi = 1.8 GeV and Tc = 240 MeV for three flavors and three colors.

arXiv comment9 pages, 3 figures; v2: renormalization of vacuum fluctuations in the linear sigma model and some references added; final version to appear in PRD

References in corpus (45)

• Chiral effective model with the Polyakov loop
• Static and Dynamic Critical Phenomena at a Second Order QCD Phase Transition
• Quark Mass and Flavour Dependence of the QCD Phase Transition
• Heavy Quark Anti-Quark Free Energy and the Renormalized Polyakov Loop
• Quark-Gluon Plasma as a Condensate of Z(3) Wilson Lines
• Hadron Resonance Mass Spectrum and Lattice QCD Thermodynamics
• Thermodynamics at Non-Zero Baryon Number Density: A Comparison of Lattice and Hadron Resonance Gas Model Calculations
• The Status of Lattice QCD at Finite Temperature
• Chiral Symmetry Restoration at Nonzero Temperature in the SU(3) \times SU(3) Linear Sigma Model
• Phenomenological Equations of State for the Quark-Gluon Plasma
• Heavy Quark Potentials in Quenched QCD at High Temperature
• Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops
• Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory
• Confinement versus Chiral Symmetry
• Event-by-Event Fluctuations from Decay of a Polyakov Loop Condensate
• The Chiral Critical Point in 3-Flavour QCD
• Renormalization in Self-Consistent Approximation schemes at Finite Temperature III: Global Symmetries
• Two flavor chiral phase transition from nonperturbative flow equations
• Where is the chiral critical point in 3-flavor QCD?
• Scaling Properties of the Energy Density in SU(2) Lattice Gauge Theory
• The O(N) Model at Finite Temperature: Renormalization of the Gap Equations in Hartree and Large-N Approximation
• Degrees of Freedom and the Deconfining Phase Transition
• Renormalization of Φ-derivable approximations in scalar field theories
• Scalar Particles in Lattice QCD
• Chiral symmetry restoration in linear sigma models with different numbers of quark flavors
• Two-point functions for SU(3) Polyakov Loops near T_c
• The equation of state for two flavor QCD at N_t=6
• QCD and the Chiral Critical Point
• Linear sigma model and chiral symmetry at finite temperature
• The K/pi ratio from condensed Polyakov loops
• Renormalizability of Phi-derivable approximations in scalar phi^4 theory
• The Deconfinement Phase Transition in One-Flavour QCD
• Light quark masses, chiral condensate and quark-gluon condensate in quenched lattice QCD with exact chiral symmetry
• Explosive Decomposition in Ultrarelativistic Heavy Ion Collision
• Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the ${\chi }^2$-method
• Explosive Collisions at RHIC?
• The Calculation of Critical Amplitudes in SU(2) Lattice Gauge Theory
• Induced Universal Properties and Deconfinement
• Covariant derivative expansion of Yang-Mills effective action at high temperatures
• One-Loop QCD Corrections to the Thermal Wilson Line Model
• Thermodynamics of the ϕ^4 theory in tadpole approximation
• Chiral Symmetry Restoration at Finite Temperature in the Linear Sigma--Model
• An Effective Action for Finite Temperature Lattice Gauge Theories with Dynamical Fermions
• The Pseudo Specific Heat in SU(2) Gauge Theory : Finite Size Dependence and Finite Temperature Effects
• Landau-Ginsberg Theory of Quark Confinement

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• Z(3) metastable states in Polyakov Quark Meson model
• Effective Lagrangians for QCD: Deconfinement and Chiral Symmetry Restoration
• Dynamical formation of center domains in quark-gluon plasma
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