# Four-loop screened perturbation theory

@article{Andersen2008FourloopSP, title={Four-loop screened perturbation theory}, author={J. Andersen and Lars T. Kyllingstad}, journal={Physical Review D}, year={2008}, volume={78}, pages={076008} }

We study the thermodynamics of massless {phi}{sup 4}-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{sup 2}, where m is the thermal mass and g is the coupling constant. The expansion is truncated at order g{sup 7} and the loop expansion is shown to have better convergence… Expand

#### 35 Citations

Pressure to order g8log g of massless ϕ4 theory at weak coupling

- Physics
- 2009

We calculate the pressure of massless 4-theory to order g8log (g) at weak coupling. The contributions to the pressure arise from the hard momentum scale of order T and the soft momentum scale of… Expand

Three-loop hard-thermal-loop free energy for QED

- Physics
- 2009

We calculate the free energy of a hot gas of electrons and photons to three loops using the hard-thermal-loop perturbation theory reorganization of finite-temperature perturbation theory. We… Expand

Renormalization of the 4PI effective action using the functional renormalization group

- Physics
- 2019

Techniques based on $n$-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum… Expand

Three-loop matching coefficients for hot QCD: reduction and gauge independence

- Physics
- 2012

A bstractWe perform an integral reduction for the 3-loop effective gauge coupling and screening mass of QCD at high temperatures, defined as matching coefficients appearing in the dimensionally… Expand

Hard-thermal-loop QED thermodynamics

- Physics
- 2010

The weak-coupling expansion for thermodynamic quantities in thermal field theories is poorly convergent unless the coupling constant is tiny. We discuss the calculation of the free energy for a hot… Expand

Two-loop HTL-resummed thermodynamics for $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

- Physics
- 2020

We compute the two-loop hard-thermal-loop (HTL) resummed thermodynamic potential for N=4 supersymmetric Yang-Mills (SYM). Our final result is manifestly gauge-invariant and was renormalized using… Expand

Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group

- Physics
- 2011

Abstract We apply to the calculation of the pressure of a hot scalar field theory a method that has been recently developed to solve the Non-Perturbative Renormalization Group. This method yields an… Expand

A brief overview of hard-thermal-loop perturbation theory

- Physics
- 2012

The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades. Here we briefly review the progress of… Expand

Three-loop HTL QCD thermodynamics

- Physics
- 2011

The hard-thermal-loop perturbation theory (HTLpt) framework is used to calculate the thermodynamic functions of a quark-gluon plasma to three-loop order. This is the highest order accessible by… Expand

Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential

- Physics
- 2016

In a previous paper (JHEP {\bf 05} (2014) 27), we calculated the three-loop thermodynamic potential of QCD at finite temperature $T$ and quark chemical potentials $\mu_q$ using the hard-thermal-loop… Expand

#### References

SHOWING 1-10 OF 54 REFERENCES

Screened perturbation theory to three loops

- Physics
- 2001

The thermal physics of a massless scalar field with a {phi}{sup 4} interaction is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding… Expand

Mass expansions of screened perturbation theory

- Physics
- 2001

The thermodynamics of massless ${\ensuremath{\varphi}}^{4}$ theory is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and… Expand

Solution to the 3-loop Φ -derivable approximation for massless scalar thermodynamics

- Physics
- 2002

We develop a systematic method for solving the 3-loop $\Phi$-derivable approximation to the thermodynamics of the massless $\phi^4$ field theory. The method involves expanding sum-integrals in powers… Expand

Resummation in hot field theories

- Physics
- 2005

Abstract There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory… Expand

Screened Perturbation Theory

- Physics
- 1997

A new perturbative scheme is proposed for the evaluation of the free energy density of field theories at finite temperature. The screened loop expansion takes into account exactly the phenomenon of… Expand

Free energy of QCD at high temperature.

- Physics, Medicine
- Physical review. D, Particles and fields
- 1996

The contribution to the free energy from the scale {ital gT} can be calculated using perturbative methods in the effective theory, but nevertheless it can be expanded in powers of {ITAL g} beginning at order{ital g}{sup 6}. Expand

Optimized perturbation theory at finite temperature

- Physics
- 1998

An optimized perturbation theory (OPT) at finite temperature $T,$ which resums higher order terms in the naive perturbation, is developed in $O(N) {\ensuremath{\varphi}}^{4}$ theory. It is proved… Expand

Hard-thermal-loop resummation of the thermodynamics of a hot gluon plasma

- Physics
- 1999

We calculate the thermodynamic functions of a hot gluon plasma to leading order in hard-thermal-loop (HTL) perturbation theory. Effects associated with screening, gluon quasiparticles, and Landau… Expand

Free energy of high temperature QED to order e5 from effective field theory.

- Physics, Medicine
- Physical review. D, Particles and fields
- 1996

An effective field theory approach makes it possible to separate contributions to the free energy from those to different momentum scales and provides an economical alternative to computations in the full theory which involves the dressing of bosonic propagators. Expand

Effective field theory approach to high-temperature thermodynamics.

- Physics, Medicine
- Physical review. D, Particles and fields
- 1995

An effective field theory approach is developed for calculating the thermodynamic properties of a field theory at high temperature $T$ and weak coupling and applies it to a massless scalar field with a $\Phi^4$ interaction. Expand