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.
We determine a next-to-leading order result for the correlator of the shear stress operator in high-temperature Yang-Mills theory. The computation is performed via an ultraviolet expansion, valid in the limit of small distances or large momenta, and
the result is used for writing operator product expansions for the Euclidean momentum and coordinate space correlators as well as for the Minkowskian spectral density. In addition, our results enable us to confirm and refine a shear sum rule originally derived by Romatschke, Son and Meyer.
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.
The pressure of QCD admits at high temperatures a factorization into purely perturbative contributions from hard thermal momenta, and slowly convergent as well as non-perturbative contributions from soft thermal momenta. The latter can be related to
various effective gluon condensates in a dimensionally reduced effective field theory, and measured there through lattice simulations. Practical measurements of one of the relevant condensates have suffered, however, from difficulties in extrapolating convincingly to the continuum limit. In order to gain insight on this problem, we employ Numerical Stochastic Perturbation Theory to estimate the problematic condensate up to 4-loop order in lattice perturbation theory. Our results seem to confirm the presence of large discretization effects, going like $aln(1/a)$, where $a$ is the lattice spacing. For definite conclusions, however, it would be helpful to repeat the corresponding part of our study with standard lattice perturbation theory techniques.
Thanks to dimensional reduction, the contributions to the hot QCD pressure coming from so-called soft modes can be studied via an effective three-dimensional theory named Electrostatic QCD (spatial Yang-Mills fields plus an adjoint Higgs scalar). The
poor convergence of the perturbative series within EQCD suggests to perform lattice measurements of some of the associated gluon condensates. These turn out, however, to be plagued by large discretization artifacts. We discuss how Numerical Stochastic Perturbation Theory can be exploited to determine the full lattice spacing dependence of one of these condensates up to 4-loop order, and sharpen our tools on a concrete 2-loop example.
