Four-loop screened perturbation theory

Abstract

We study the thermodynamics of massless phi-fourth theory using screened perturbation theory. In this method, the perturbative expansion is reorganized by adding and subtracting a thermal mass term in the Lagrangian. We calculate the free energy through four loops expanding in a double power expansion in m/T and g^2, where m is the thermal mass and g is the coupling constant. The expansion is truncated at order g^7 and the loop expansion is shown to have better convergence properties than the weak-coupling expansion. The free energy at order g^6 involves the four-loop triangle sum-integral evaluated by Gynther, Laine, Schroeder, Torrero, and Vuorinen using methods developed by Arnold and Zhai. The evaluation of the free energy at order g^7 requires the evaluation of a nontrivial three-loop sum-integral, which we calculate by the same methods.

34 pages, 6 figures, RevTeX

References in corpus (50)

• The Quark-Gluon Plasma in Equilibrium
• Free Energy of QCD at High Temperature
• Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma. I. Entropy and density
• Effective Field Theory Approach to High-Temperature Thermodynamics
• The Three-Loop Free Energy for Pure Gauge QCD
• The Three-Loop Free Energy for High-Temperature QED and QCD with Fermions
• The Free Energy of Hot Gauge Theories with Fermions Through g^5
• Screened Perturbation Theory
• Hard-thermal-loop Resummation of the Free Energy of a Hot Gluon Plasma
• The entropy of the QCD plasma
• The Nonabelian Debye Mass at Next-to-Leading Order
• Advances in perturbative thermal field theory
• Optimized Perturbation Theory at Finite Temperature
• Variational perturbation expansion for strong-coupling coefficients of the anharmonic oscillator
• Nonperturbative renormalization for 2PI effective action techniques
• Resummation in Hot Field Theories
• Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory
• HTL Perturbation Theory to Two Loops
• Renormalization of Self-consistent Approximation schemes Finite Temperature II: Applications to the Sunset Diagram
• Self-consistent hard-thermal-loop thermodynamics for the quark-gluon plasma
• Five-loop renormalization group functions of $O(n)$-symmetric ${\varphi }^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$
• Hard-thermal-loop Resummation of the Thermodynamics of a Hot Gluon Plasma
• Renormalization of Φ-derivable approximations in scalar field theories
• Screened Perturbation Theory to Three Loops
• Hard-thermal-loop Resummation of the Free Energy of a Hot Quark-Gluon Plasma
• Gauge-fixing dependence of Phi-derivable approximations
• Four-loop vacuum energy density of the SU(N_c) + adjoint Higgs theory
• Renormalized thermodynamics from the 2PI effective action
• A Nonperturbative Study of Inverse Symmetry Breaking at High Temperatures
• Renormalizability of Phi-derivable approximations in scalar phi^4 theory
• Two-loop HTL Thermodynamics with Quarks
• HTL Resummation of the Thermodynamic Potential
• Four-loop pressure of massless O(N) scalar field theory
• Mass Expansions of Screened Perturbation Theory
• 2PI effective action and gauge invariance problems
• The Pressure of Hot $g^2{\varphi }^4$ Theory at order $g^5$
• High Temperature Resummation in the Linear $\delta$-Expansion
• The Free Energy of Hot QED at Fifth Order
• Four-Loop Vacuum Energy Beta Function in O(N) Symmetric Scalar Theory
• Solution to the 3-Loop $\Phi$-Derivable Approximation for Massless Scalar Thermodynamics
• Higher Order Corrections to the Equation of State of QED at High Temperature
• Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase
• Solution to the 3-loop $\Phi$-derivable Approximation for Scalar Thermodynamics
• Three-loop Phi-derivable Approximation in QED
• The Three Loop Equation of State of QED at High Temperature
• Study of the O(N) linear sigma model at finite temperature using the 2PPI expansion
• The pressure of QED from the two-loop 2PI effective action
• The Free Energy of High Temperature QED to Order $e^5$ From Effective Field Theory
• A 2 Loop 2PPI Analysis of $\lambda {\varphi }^4$ at Finite Temperature
• Non-perturbative calculations of a global U(1) theory at finite density and temperature

Cited by in corpus (33)

• Three-loop HTLpt thermodynamics at finite temperature and chemical potential
• Theoretical uncertainties for cosmological first-order phase transitions
• Perturbative Thermal QCD: Formalism and Applications
• Three-loop HTL QCD thermodynamics
• Gluon Thermodynamics at Intermediate Coupling
• Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential
• Optimized perturbation theory for charged scalar fields at finite temperature and in an external magnetic field
• The 2PI effective theory at next-to-leading order using the functional renormalization group
• Pressure to order $g^8\ast log(g)$ in ${\varphi }^4$-theory at weak coupling
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• A brief overview of hard-thermal-loop perturbation theory
• Renormalization Group Optimized Perturbation Theory at Finite Temperatures
• Three-loop HTL Free Energy for QED
• Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group
• Three-loop HTLpt thermodynamics at finite temperature and chemical potential
• A new method for taming tensor sum-integrals
• Resummation scheme for 3d Yang-Mills and the two-loop magnetic mass for hot gauge theories
• QCD pressure: renormalization group optimized perturbation theory confronts lattice
• Three loop HTL perturbation theory at finite temperature and chemical potential
• Two-loop HTL-resummed thermodynamics for N=4 supersymmetric Yang-Mills theory
• Renormalization of the 4PI effective action using the functional renormalization group
• Recent progress in hard-thermal-loop QCD thermodynamics and collective excitations
• Renormalization group improved pressure for hot and dense quark matter
• On the (in)consistency of perturbation theory at finite temperature
• Renormalization group optimized $\lambda {\varphi }^4$ pressure at next-to-next-to-leading order
• Equation of State for QCD at finite temperature and density. Resummation versus lattice data
• Pressure of massless hot scalar theory in the boundary effective theory framework
• Effective potential in the BET formalism
• Non-perturbative constraints on perturbation theory at finite temperature
• Hard thermal contributions to phase transition observables at NNLO
• Scheme dependence of two-loop HTLpt-resummed ${\text{SYM}}_{4,4}$ thermodynamics
• Hard-thermal-loop QED thermodynamics
• Screened perturbation theory at four loops