Related papers: On the new method of computing two-loop massive di…
We provide analytic results for two-loop four-point master integrals with one massive propagator and one massive leg relevant to single top production. Canonical bases of master integrals are constructed and the Simplified Differential…
We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative…
The direct computation method(DCM) is developed to calculate the multi-loop amplitude for general masses and external momenta. The ultraviolet divergence is under control in dimensional regularization. In this paper we report on the…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
We show that the problem of solving recurrence relations for L-loop (R+1)-point Feynman integrals within the method of integration by parts is equivalent to the corresponding problem for (L+R)-loop vacuum or (L+R-1)-loop propagator-type…
In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…
Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the vector flavor-nonsinglet contribution to deeply-virtual Compton scattering (DVCS). The analytic expression for the coefficient function in…
In this paper we present a novel technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. In order to extract…
The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for…
Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals…
We propose a novel local subtraction scheme for the computation of Next-to-Leading Order contributions to theoretical predictions for scattering processes in perturbative Quantum Field Theory. With respect to well known schemes proposed…
In higher order calculations a number of new technical problems arise: one needs diagrams in arbitrary dimension in order to obtain their needed $\epsilon$-expansion, zero Gram determinants appear, renormalization produces diagrams with…
A number of exact results for two-loop three-point diagrams with massless internal particles and arbitrary (off-shell) external momenta are presented. Divergent contributions are calculated in the framework of dimensional regularization.
For certain dimensionally-regulated massive two- and three-loop propagator-type diagrams the higher order epsilon-expansion is constructed.
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…
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…
We use dimensional recurrence relations and analyticity to calculate four-loop propagator-type master integrals in the heavy-quark effective theory. Compared to previous applications of the DRA method, we apply a new technique of fixing…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
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…
We consider the two-loop massless propagator-type Feynman diagram with an arbitrary (non-integer) index on the central line. We analytically prove the equality of the two well-known results existing in the literature which express this…