Related papers: New representation of the two-loop crossed vertex …
We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for $pp \rightarrow t\bar{t}j$. We derive differential equations for the master integrals by solving the…
A two-replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are associated with the percolation threshold of the graphical…
In this paper we introduce the theory of derivatives of moments and (moment) functionals to represent moment functionals by Gaussian mixtures, characteristic functions of polytopes, and simple functions of polytopes. We study, among other…
The two-loop Euler-Heisenberg-type effective action for N = 1 supersymmetric QED is computed within the background field approach. The background vector multiplet is chosen to obey the constraints D_\a W_\b = D_{(\a} W_{\b)} = const, but is…
Using techniques of conformal bootstrap, we propose analytical expressions for a large class of two-point functions of bulk fields in critical loop models defined on the upper-half plane. Our results include the two-point connectivities in…
Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…
When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…
We compute the two-loop master integrals for non-leptonic heavy-to-heavy decays analytically in a recently-proposed canonical basis. For this genuine two-loop, two-scale problem we first derive a basis for the master integrals that…
The 2-dimensional U(1) gauge-Higgs model with a topological term is a simple example of a lattice field theory where the complex action problem comes from the topological term. We show that the model can be exactly rewritten in terms of…
An algorithm to construct analytic approximations to two-loop diagrams describing their behaviour at small non-zero thresholds is discussed. For some special cases (involving two different-scale mass parameters), several terms of the…
One-loop two-, three- and four-point scalar functions are analytically integrated directly such that they are expressed in terms of Lauricella's hypergeometric function $F_D$. For two- and three-point functions, exact expressions are…
The three-loop corrections to the potential of two heavy quarks are computed. Analytic results for the most complicated master integrals are presented.
An impressive effort is being placed in order to develop new strategies that allow an efficient computation of multi-loop multi-leg Feynman integrals and scattering amplitudes, with a particular emphasis on removing spurious singularities…
We present a brief description of the light-cone gauge calculation of the spin-dependent next-to-leading order splitting functions.
The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master…
In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of…
We introduce the notion of a cross-frame potential function, which takes one frame as input and returns its cross-frame potential value with respect to another frame. We analyze the behavior of this new function to determine what…
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…
In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…
We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of…