Related papers: Reduction of one-loop integrals with higher poles …

Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower…

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…

Recently we showed how, in two-dimensional scalar theories, one-loop threshold diagrams can be cut into the product of one or more tree-level diagrams arXiv:2206.09368. Using this method on the ADE series of Toda models, we computed the…

We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional…

The two-loop contributions are now often required by the precision experiments, yet are hard to express analytically while keeping precision. One way to approach this challenging task is via the dispersive approach, allowing to replace…

In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described. As…

We report on a technique for evaluating finite unitarity cut for one-loop amplitudes in gauge theories, and discuss its application to the cut-constructible part of six-gluon amplitude in QCD.

We develop a manifestly supersymmetric version of the generalized unitarity cut method for calculating scattering amplitudes in N=4 SYM theory. We illustrate the power of this method by computing the one-loop n-point NMHV super-amplitudes.…

In this article we present a method to generate analytic expressions for the integral coefficients of loop amplitudes using numerical evaluations only. We use high-precision arithmetic to explore the singularity structure of the…

We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the…

The massless one-loop box integral with arbitrary indices in arbitrary space-time dimension $d$ is shown to reduce to a sum over three generalised hypergeometric functions. This result follows from the solution to the third order…

Unitarity cuts of enhanced Pomeron diagrams are analyzed in the framework of the Reggeon Field Theory. Assuming the validity of the Abramovskii-Gribov-Kancheli cutting rules, we derive a complete set of cut non-loop enhanced graphs and…

We propose an alternative approach based on series representation to directly reduce multi-loop multi-scale scattering amplitude into set of freely chosen master integrals. And this approach avoid complicated calculations of inverse matrix…

We present the universal one-loop effective action for all operators of dimension up to six obtained by integrating out massive, non-degenerate multiplets. Our general expression may be applied to loops of heavy fermions or bosons, and has…

An explicit Loop Tree Duality (LTD) formula for two-loop Feynman integrals with integer power of propagators is presented and used for a numerical UV divergence subtraction algorithm. This algorithm proceeds recursively and it is based on…

We demonstrate that the use of analytical on-shell methods involving calculation of the discontinuity across the t-channel cut associated with the exchange of a pair of massless particles (photons or gravitons) can be used to evaluate…

We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…

Recutting is an operation on planar polygons defined by cutting a polygon along a diagonal to remove a triangle, and then reattaching the triangle along the same diagonal but with opposite orientation. Recuttings along different diagonals…

In this paper, new schemes for a squarer, multiplier and divider of complex numbers are proposed. Traditional structural solutions for each of these operations require the presence some number of general-purpose binary multipliers. The…

We present a systematic method to determine BCJ numerators for one-loop amplitudes that explores the global constraints on the loop momentum dependence. We apply this method to amplitudes in N=4 gauge theory, working out detailed examples…