Related papers: A fresh look on three-loop sum-integrals

We report on the computation of a class of massless bosonic three-loop vacuum sum-integrals which are key building blocks for an evaluation of the Debye screening mass in hot QCD. Generalizing known techniques and introducing the concept of…

Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak…

We derive analytic results for scalar massless bosonic vacuum sum-integrals at two loops. Building upon a recent factorization proof of massive two-loop vacuum integrals, we are able to solve the corresponding Matsubara sums and map the…

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.

This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their…

We discuss the systematic evaluation of 3-loop vacuum integrals with arbitrary masses. Using integration by parts, the general integral of this type can be reduced algebraically to a few basis integrals. We define a set of modified finite…

Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence…

The approach to the constructing explicit solutions of the recurrence relations for multi-loop integrals are suggested. The resulting formulas demonstrate a high efficiency, at least for 3-loop vacuum integrals case. They also produce a new…

Explicit formulas for solutions of recurrence relations for 3--loop vacuum integrals are generalized for the $n$-loop case.

The implementation of an algorithm for three-loop massive vacuum integrals, based on the explicit solution of the recurrence relations, in REDUCE and FORM is described.

We introduce a new framework for perturbatively computing equilibrium thermodynamic properties of cosmological phase transitions to high loop orders, using the full four-dimensional resummed thermal effective potential and avoiding the…

We study the applicability of the Z-Sum approach to multi-loop calculations with massive particles in perturbative quantum field theory. We systematically analyze the case of one-loop scalar integrals, which represent the building blocks of…

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…

We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…

We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. We also construct the basis of irrational constants being harmonic polylgarithms of arguments $e^{k i \pi/3}$.

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…

A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…

This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…

We establish estimates for linear correlation sums involving sums of three positive integral cubes. Under appropriate conditions, the underlying methods permit us to establish the solubility of systems of homogeneous linear equations in…

We consider the scalar sector of a general renormalizable theory and evaluate the effective potential through three loops analytically. We encounter three-loop vacuum bubble diagrams with up to two masses and six lines, which we solve using…