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This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…
Near full-null degenerate singular points of analytic vector fields, asymptotic behaviors of orbits are not given by eigenvectors but totally decided by nonlinearities. Especially, in the case of high full-null degeneracy, i.e., the lowest…
We calculate the unpolarized and polarized two--loop massless off--shell operator matrix elements in QCD to $O(\varepsilon)$ in the dimensional parameter in an automated way. Here we use the method of arbitrary high Mellin moments and…
A comprehensive study is performed of two-loop Feynman diagrams with three external legs which, due to the exchange of massless gauge-bosons, give raise to infrared and collinear divergencies. Their relevance in assembling realistic…
The soft radiation emitted in jet cross sections can resolve the directions and colors of individual hard partons, leading to a complicated pattern of logarithmically enhanced terms in the perturbative series. Starting from a factorization…
In order to meet the precision requirements for the LHC and future colliders, next-to-next-to-leading order corrections to a wide range of processes are essential, making general automated tools highly desirable. Extending the strategy of…
One of the main difficulties in studying Quantum Field Theory, in the perturbative regime, is the calculation of D-dimensional Feynman integrals. In general, one introduces the so-called Feynman parameters and associated with them the…
An analytical approach is applied to the calculation of some dimensionally-regulated two-loop vertex diagrams with essential on-shell singularities. Such diagrams are important for the evaluation of QED corrections to the muon decay, QCD…
An asymptotic expansion of the two-loop two-point ``master'' diagram with two masses $m$ and $M$, on the mass shell $Q^2=M^2$, is presented. The treatment of the non-analytical terms arising in the expansion around the branching point is…
I obtain identities satisfied by the 3-loop self-energy master integrals with four or five propagators with generic masses, including the derivatives with respect to each of the squared masses and the external momentum invariant. These…
The irreducible tensor operators and their tensor products employing Racah algebra are studied. Transformation procedure of the coordinate system operators act on are introduced. The rotation matrices and their parametrization by the…
Belokurov-Usyukina loop reduction method has been proposed in 1983 to reduce a number of rungs in triangle ladder-like diagram by one. The disadvantage of the method is that it works in d=4 dimensions only and it cannot be used for…
We provide the reader with a (very) short review of recent advances in our understanding of the $\pi$-dependent terms in massless (Euclidean) 2-point functions as well as in generic anomalous dimensions and $\beta$-functions. We extend the…
We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
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 a new method of calculating scalar propagator and vertex functions in the two-loop approximation, for arbitrary masses of particles. It is based on a double integral representation, suitable for numerical evaluation. Real and…
I study the Feynman integrals needed to compute two-loop self-energy functions for general masses and external momenta. A convenient basis for these functions consists of the four integrals obtained at the end of Tarasov's recurrence…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor representations of finite and infinite symmetric groups into…