Higher-order corrections to the equation-of-state of QED at high temperature

Abstract

We elaborate on the computation of the pressure of thermal quantum electrodynamics, with massless electrons, to the fifth (e 5 ) order. The calculation is performed within the Feynman gauge and the imaginary-time formalism is employed. For the e 4 calculation, the method of Sudakov decomposition is used to evaluate some ultraviolet finite integrals which have a collinear singularity. For the e 5 contribution, we give an alternative derivation and extend the discussion to massive electrons and nonzero chemical potential. Comments are made on expected similarities and differences for prospective three-loop calculations in QCD. *

Three-loop HTL gluon thermodynamics at intermediate coupling

“…The calculation of thermodynamic functions using weakly-coupled quantum field theory has a long history [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The QCD free energy is known up to order g 6 log(g); however, the resulting weak-coupling approximations do not converge at phenomenologically relevant couplings.…”

Loops for Hot QCD

“…There is an important class of relations between fermionic and bosonic sum-integrals, which can be derived by partitioning the Matsubara sums and then rescaling spatial integration momenta on the left-hand-side as p i → 1 2 p i (see, e.g., [7]). …”

A Brief Overview of Hard-Thermal-Loop Perturbation Theory

“…In the early 1990s the free energy was calculated to order g 4 for massless scalar φ 4 theory [10,11], quantum electrodynamics (QED) [12] and QCD [11,12], respectively. The corresponding calculations to order g 5 were obtained soon afterwards [13][14][15][16][17][18][19][20]. Recent results have extended the calculation of the QCD free energy by determining the coefficient of the g log g contribution [21].…”