Related papers: A new three-loop sum-integral of mass dimension tw…
A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…
The Debye screening mass for a quark-gluon plasma at high temperature is calculated to next-to-leading order in the QCD coupling constant from the correlator of two Polyakov loops. The result agrees with the screening mass defined by the…
I present analytical expressions for the cusp anomalous dimension in QCD through three loops in terms of elementary functions and ordinary polylogarithms. I observe interesting relations between the results at different loops and provide a…
We compute the matching coefficients between QCD and non-relativistic QCD for external vector, axial-vector, scalar and pseudo-scalar currents up to three-loop order. We concentrate on the non-singlet contributions and present precise…
We report on recent progress on five-loop calculations in perturbative QCD. We discuss the computation of the perturbative quark condensate, decoupling in QCD, and the precision determination of charm and bottom quark masses. For the…
We present for numerical use the analytic continuations to complex arguments of those basic Mellin transforms, which build the harmonic sums contributing to the 3--loop anomalous dimensions. Eight new basic functions contribute in addition…
We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be…
As a generalization of a previous work [Phys. Rev. D. {\bf 59}, 105014 (1999)], we compute analytically a class of three-loop vacuum diagrams with two {\em arbitrarily} different mass scales. We use a decomposition algorithm in which the…
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…
We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by…
In this contribution we discuss new features of SecDec-3.0, a public program for the evaluation of dimensionally-regulated parametric integrals using sector decomposition. We will focus on two main aspects: the implementation of an improved…
QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the $\bar{MS}$ scheme. Both the high and the low energy expansion of the vector current correlator are involved…
In the effective theory for the deconfining phase of SU(2) Yang-Mills thermodynamics we compute estimates for the moduli of the irreducible three-loop diagrams contributing to the pressure. Our numerical results are in agreement with…
We present an alternative way to calculate the screening of the static potential between two charges in (non)abelian gauge theories at high temperatures. Instead of a loop expansion of a gauge boson self-energy, we evaluate the energy shift…
Coupled 1-loop gap equations are studied numerically for non-Abelian electric and magnetic screening in various versions of the three-dimensional effective gauge models. Corrections due to higher dimensional and non-local operators are…
In this letter we present a high-precision evaluation of the expansions in eps=(3-d)/2 of (up to) four-loop scalar vacuum master integrals, using the method of difference equations developed by Laporta. We cover the complete set of fully…
We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general…
We analyze 3-loop contributions to the gauge coupling felt by ultrasoft ("magnetostatic") modes in hot Yang-Mills theory. So-called soft/hard terms, originating from dimension-six operators within the soft effective theory, are shown to…
The Debye mass m_D is computed nonperturbatively in the deconfined phase of QCD, where chromomagnetic confinement is known to be present. The latter defines m_D to be m_D=c_D\sqrt{\sigma_s}, where c_D \approx 2 and \sigma_s=\sigma_s(T) is…
Recent Developments in computing very specific helicity amplitudes in two loop QCD are presented. The techniques focus upon the singular structure of the amplitude rather than on a diagramatic and integration approach