Related papers: IR finite one-loop box scalar integral with massle…
We report on an approach to integration-by-parts reduction based on Gr\"obner bases. We establish the underlying noncommutative rational double-shift algebra wherein the integration-by-parts relations form a left ideal. We describe in…
In the recent years there has been an enormous development in the evaluation of higher order quantum corrections. An essential ingredient in the practical calculations is provided by vacuum diagrams, i.e. integrals without external momenta.…
In this paper we derive some basic results of circuit theory using `Implicit Linear Algebra' (ILA). This approach has the advantage of simplicity and generality. Implicit linear algebra is outlined in [1]. We denote the space of all vectors…
The soft and collinear singularities of general scalar and tensor one-loop N-point integrals are worked out explicitly. As a result a simple explicit formula is given that expresses the singular part in terms of 3-point integrals. Apart…
To get the total cross section of one interaction from its amplitude ${\cal M}$, one needs to integrate $|{\cal M}|^2$ over phase spaces of all out-going particles. Starting from this paper, we will propose a new method to perform such…
We present a simple method which simplifies the evaluation of the on-shell multiple box diagrams reducing them to triangle type ones. For the $L$-loop diagram one gets the expression in terms of Feynman parameters with $2L$-fold…
A method to isolate the poles of dimensionally regulated multi-loop integrals and to calculate the pole coefficients numerically is extended to be applicable to phase space integrals as well.
In phenomenological models with D-branes, there are in general open-string massless scalar fields, in addition to closed-string massless moduli fields corresponding to the compactification. It is interesting to focus on the fate of such…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
We calculate analytically the three-loop planar master integrals relevant for heavy-to-light form factors using the method of differential equations. After choosing a proper canonical basis, the boundary conditions are easy to be…
An account is given of how the 'box integrals', as used for one-loop calculations in massless field theory, appear in momentum-twistor geometry. Particular attention is paid to the role of compact contour integration in representing the…
We present a complete reimplementation of the LinearSystem package of Magma, with substantial improvements in design and performance. The resulting efficiency enables computations that were previously out of reach. We briefly describe the…
Mellin-Barnes integral representation of one-loop off-shell box massless diagram is five-fold by construction. On the other hand, it is known from the year 1992 that it may be reduced to certain two-fold Mellin-Barnes integral. We propose a…
A method is presented for obtaining the $\epsilon$-expansion for on-shell massless scalar double-box diagram.
We recently presented a new method for the evaluation of one-loop amplitude of arbitrary scattering processes, in which the reduction to scalar integrals is performed at the integrand level. In this talk, we review the main features of the…
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…
We provide high-energy approximations for all one-loop scalar 3- and 4-point functions and the corresponding tensor integrals that appear in scattering processes with four external on-shell particles. Our expressions are valid if all…
We compute the one-loop potential (the Casimir energy) for scalar, spinor and vectors fields on the spaces $\,R^{m+1}\, \times\,Y$ with $\,Y=\,S^N\,,CP^2$. As a physical model we consider spinor electrodynamics on four-dimensional product…
We explicitly construct a class of multivariate generalized hypergeometric series which is conjectured in our previous paper [Alkalaev & Mandrygin 2025] to calculate multipoint one-loop parametric conformal integrals in $D$ dimensions. Our…
Several interesting formulas concerning finite Hilbert transform and logarithmic integrals are proved with application in determining equilibrium measures, planar limits of analytic random matrix models with $1-$cut potential and solving…