Scale Invariant Resummed Perturbation at Finite Temperatures

Abstract

We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories. The resulting convergence and scale dependence of optimized thermodynamical quantities, here illustrated up to two-loop order, are drastically improved as compared to standard perturbative expansions, as well as to other related methods such as the screened perturbation or (resummed) hard-thermal-loop perturbation, that miss RG invariance as we explain. Being very general and easy to implement, our method is a potential analytical alternative to deal with the phase transitions of field theories such as thermal QCD.

5 pages, 1 figure. v2: additional explanations on the generically improved scale invariance at higher orders, typos corrected, figure quality improved, to appear in Phys.Rev.Lett

References in corpus (15)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The QCD transition temperature: results with physical masses in the continuum limit
• The QCD Equation of State with almost Physical Quark Masses
• The transition temperature in QCD
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops
• Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
• Three-loop HTL gluon thermodynamics at intermediate coupling
• Thermodynamics and Phase Structure of the Two-Flavor Nambu--Jona-Lasinio Model Beyond Large-N_c
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops
• Multiple Critical Points in Effective Quark Models
• The chiral condensate from renormalization group optimized perturbation
• Applicability of the Linear delta Expansion for the lambda phi^4 Field Theory at Finite Temperature in the Symmetric and Broken Phases
• Dynamical Generation of a Repulsive Vector Contribution to the Quark Pressure
• Renormalization Group Optimized Perturbation Theory at Finite Temperatures
• Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group

Cited by in corpus (18)

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• Chiral matrix model of the semi-Quark Gluon Plasma in QCD
• Three-loop HTLpt thermodynamics at finite temperature and chemical potential
• Reliability of the optimized perturbation theory in the 0-dimensional $O(N)$ scalar field model
• Non-strange quark stars within resummed QCD
• All order resummed leading and next-to-leading soft modes of dense QCD pressure
• Renormalization group improved pressure for cold and dense QCD
• Interplay Between Approximation Theory and Renormalization Group
• QCD pressure: renormalization group optimized perturbation theory confronts lattice
• Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
• Optimized perturbation theory applied to the study of the thermodynamics and BEC-BCS crossover in the three-color Nambu--Jona-Lasinio model
• Asymptotically Free Theory with Scale Invariant Thermodynamics
• Renormalization group improved pressure for hot and dense quark matter
• Renormalization group optimized $\lambda {\varphi }^4$ pressure at next-to-next-to-leading order
• Cold Quark Matter: Renormalization Group Improvement at next-to-next-to leading order
• Comparing strange and non-strange quark stars within resummed QCD at NLO
• Cosmological constant as a finite temperature effect
• Scale dependence improvement of the quartic scalar field thermal effective potential in the optimized perturbation theory