Renormalization group optimized $\lambda {\varphi }^4$ pressure at next-to-next-to-leading order

Abstract

We investigate the renormalization group optimized perturbation theory (RGOPT) at the next-to-next-to-leading order (NNLO) for the thermal scalar field theory. From comparing three thus available successive RGOPT orders we illustrate the efficient resummation and very good apparent convergence properties of the method. In particular the remnant renormalization scale dependence of thermodynamical quantities is drastically improved as compared to both standard perturbative expansions and other related resummation methods, such as the screened perturbation theory. Our present results thus constitute a useful first NNLO illustration in view of NNLO applications of this approach to the more involved thermal QCD.

arXiv comment18 pages, 8 figures

References in corpus (46)

• 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
• Resummation in a Hot Scalar Field Theory
• The transition temperature in QCD
• Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma. I. Entropy and density
• Effective Field Theory Approach to High-Temperature Thermodynamics
• Basics of thermal field theory -- a tutorial on perturbative computations
• The Three-Loop Free Energy for Pure Gauge QCD
• Screened Perturbation Theory
• Hard-thermal-loop Resummation of the Free Energy of a Hot Gluon Plasma
• Three-loop HTLpt thermodynamics at finite temperature and chemical potential
• Advances in perturbative thermal field theory
• Nonperturbative renormalization for 2PI effective action techniques
• Resummation in Hot Field Theories
• Three-loop HTL QCD thermodynamics
• Introductory lectures on lattice QCD at nonzero baryon number
• Screened Perturbation Theory to Three Loops
• Three-loop HTLpt Pressure and Susceptibilities at Finite Temperature and Density
• Hard-thermal-loop Resummation of the Free Energy of a Hot Quark-Gluon Plasma
• Equation of State of hot and dense QCD: Resummed perturbation theory confronts lattice data
• Gluon Thermodynamics at Intermediate Coupling
• Renormalized thermodynamics from the 2PI effective action
• Foam Diagram Summation at Finite Temperature
• Three-loop HTL gluon thermodynamics at intermediate coupling
• Thermodynamics of the high-temperature quark-gluon plasma
• Mass Expansions of Screened Perturbation Theory
• The Pressure of Hot $g^2{\varphi }^4$ Theory at order $g^5$
• Four-loop screened perturbation theory
• Strong-Coupling ${\varphi }^4$-Theory in $4-\epsilon$ Dimensions and Critical Exponents
• α_S from $F_{\pi }$ and Renormalization Group Optimized Perturbation
• The Massive Thermal Basketball Diagram
• The chiral condensate from renormalization group optimized perturbation
• Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model
• Applicability of the Linear delta Expansion for the lambda phi^4 Field Theory at Finite Temperature in the Symmetric and Broken Phases
• Four-Loop Vacuum Energy Beta Function in O(N) Symmetric Scalar Theory
• Five-Loop Vacuum Energy Beta Function in phi^4 Theory with O(N)-Symmetric and Cubic Interactions
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• Renormalization Group Optimized Perturbation Theory at Finite Temperatures
• Scale Invariant Resummed Perturbation at Finite Temperatures
• Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group
• Renormalization group improved pressure for cold and dense QCD
• 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
• Asymptotically Free Theory with Scale Invariant Thermodynamics
• Massive renormalization scheme and perturbation theory at finite temperature
• Renormalization group improved pressure for hot and dense quark matter

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• Non-strange quark stars within resummed QCD
• Comparing strange and non-strange quark stars within resummed QCD at NLO
• Cold Quark Matter: Renormalization Group Improvement at next-to-next-to leading order
• Scale dependence improvement of the quartic scalar field thermal effective potential in the optimized perturbation theory