We give a short review on recent progress in the field of automated calculations in finite-temperature field theory, where integration-by-parts techniques have proven (almost) as useful as in the zero-temperature case. Furthermore, we provide one con
crete example of an evaluation of a new three-loop master sum-integral that exhibits maximal divergence.
We evaluate a new 3-loop sum-integral which contributes to the Debye screening mass in hot QCD. While we manage to derive all divergences analytically, its finite part is mapped onto simple integrals and evaluated numerically.
In order to prepare the ground for evaluating classes of three-loop sum-integrals that are presently needed for thermodynamic observables, we take a fresh and systematic look on the few known cases, and review their evaluation in a unified way using
coherent notation. We do this for three important cases of massless bosonic three-loop vacuum sum-integrals that have been frequently used in the literature, and aim for a streamlined exposition as compared to the original evaluations. In passing, we speculate on options for generalization of the computational techniques that have been employed.
We demonstrate the applicability of integration-by-parts (IBP) identities in finite-temperature field theory. As a concrete example, we perform 3-loop computations for the thermodynamic pressure of QCD in general covariant gauges, and confirm earlier Feynman-gauge results.
Electroweak precision measurements, encoded in the oblique parameters, give strong constraints on physics beyond the Standard Model. The oblique parameters S, T, U (V, W, X) are calculated in the next-to-minimal supersymmetric model (NMSSM). We outli
ne the calculation of the oblique parameters in terms of one-loop gauge-boson selfenergies and find sensitive restrictions for the NMSSM parameter space.
Perturbation theory for non-Abelian gauge theories at finite temperature is plagued by infrared divergences caused by magnetic soft modes $sim g^2T$, which correspond to the fields of a 3d Yang-Mills theory. We revisit a gauge invariant resummation s
cheme to solve this problem by self-consistent mass generation using an auxiliary scalar field, improving over previous attempts in two respects. First, we generalise earlier SU(2) treatments to SU(N). Second, we obtain a gauge independent two-loop gap equation, correcting an error in the literature. The resulting two-loop approximation to the magnetic mass represents a $sim 15%$ correction to the leading one-loop value, indicating a reasonable convergence of the resummation.
In this talk, I present the status of attempts to analyze the behavior of the so-called spatial t Hooft loop, which can be taken as an order parameter for the deconfinement phase transition in pure SU(N) gauge theory. While lattice data show a striki
ngly universal scaling of extracted k-string tensions for various values of k and N, the analytic approach to these observables might need some refinement.
