Quark Number Susceptibility, Thermodynamic Sum Rule, and Hard Thermal Loop Approximation

Abstract

The quark number susceptibility, associated with the conserved quark number density, is closely related to the baryon and charge fluctuations in the quark-gluon plasma, which might serve as signature for the quark-gluon plasma formation in ultrarelativistic heavy-ion collisions. Beside QCD lattice simulations, the quark number susceptibility has been calculated recently using a resummed perturbation theory (Hard Thermal Loop resummation). In the present work we show, based on general arguments, that the computation of this quantity neglecting Hard Thermal Loop vertices contradicts the Ward identity and violates the thermodynamic sum rule following from the quark number conservation. We further show that the Hard Thermal Loop perturbation theory is consistent with the thermodynamic sum rule.

4 pages, 2 figures, final version to be published in Phys. Rev. D

References in corpus (27)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• Fluctuation Probes of Quark Deconfinement
• Charged Particle Ratio Fluctuation as a Signal for QGP
• Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma. I. Entropy and density
• Chiral Restoration in Hot and/or Dense Matter
• Screened Perturbation Theory
• Hard-thermal-loop Resummation of the Free Energy of a Hot Gluon Plasma
• The entropy of the QCD plasma
• Event-by-event fluctuations of average transverse momentum in central Pb+Pb collisions at 158 GeV per nucleon
• Quark number susceptibilities from HTL-resummed thermodynamics
• HTL Perturbation Theory to Two Loops
• Self-consistent hard-thermal-loop thermodynamics for the quark-gluon plasma
• Hard-thermal-loop Resummation of the Thermodynamics of a Hot Gluon Plasma
• Hard-thermal-loop Resummation of the Free Energy of a Hot Quark-Gluon Plasma
• Gauge-fixing dependence of Phi-derivable approximations
• Quark number susceptibilities of hot QCD up to g^6ln(g)
• Susceptibilities and screening masses in two flavor QCD
• Finite Temperature Meson Correlation Functions in HTL Approximation
• Quark number susceptibilities, strangeness and dynamical confinement
• Quark Number Susceptibility in Hard Thermal Loop Approximation
• The continuum limit of quark number susceptibilities
• The Equation of State for Dense QCD and Quark Stars
• Quark Dispersion Relation and Dilepton Production in the Quark-Gluon Plasma
• A precise determination of T_c in QCD from scaling
• Comparing different hard-thermal-loop approaches to quark number susceptibilities
• Chiral Susceptibility in Hard Thermal Loop Approximation
• Isospin Fluctuations in QCD and Relativistic Heavy-Ion Collisions

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• Three-loop HTLpt Pressure and Susceptibilities at Finite Temperature and Density
• Two-loop HTL pressure at finite temperature and chemical potential
• Simple patterns for non-linear susceptibilities near T_c
• Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential
• Fluctuation of strongly interacting matter in Polyakov Nambu Jona-Lasinio model in finite volume
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• Dilepton rate and quark number susceptibility with the Gribov action
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• Polyakov--Nambu--Jona-Lasinio model in finite volumes
• Three-loop HTLpt thermodynamics at finite temperature and chemical potential
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• Isospin symmetry breaking and baryon-isospin correlations from Polyakov$-$Nambu$-$Jona-Lasinio model
• Selfconsistent approximations, symmetries and choice of representation
• Hard Thermal Loop -- theory and applications
• The Quark Number Susceptibility in Hard-Thermal-Loop Approximation
• Continuum study of various susceptibilities within thermal QED${}_3$
• Quark Number Susceptibility : Revisited with Fluctuation-Dissipation Theorem in mean field theories
• Second-order quark number susceptibility of deconfined QCD matter in the presence of a magnetic field
• QCD mesonic screening masses using Gribov quantization
• Finite temperature QCD four-point function in the presence of a weak magnetic field within the hard thermal loop approximation
• Recent progress in hard-thermal-loop QCD thermodynamics and collective excitations
• The Equation of State and Quark Number Susceptibility in Hard-Dense-Loop Approximation
• A consistent quasiparticle picture of Quark-Gluon plasma and the velocity of sound
• Study of net-baryon higher moments in PNJL model and their expectation for net-proton using the Subensemble Acceptance Method for the search of QCD critical point
• Non-perturbative study of spectral function and its application in Quark Gluon Plasma