Related papers: Universal Decomposition of Phase-Space Integrands
The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical…
One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators…
We explicitly construct a large class of unitary transformations that allow to perform the ideal estimation of the phase-shift on a single-mode radiation field. The ideal phase distribution is obtained by heterodyne detection on two…
This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results…
We outline the concrete steps involved in building prescriptive master integrand bases for scattering amplitudes beyond the planar limit. We highlight the role of contour choices in such bases, and illustrate the full process by…
We present a program for the numerical evaluation of multi-dimensional polynomial parameter integrals. Singularities regulated by dimensional regularisation are extracted using iterated sector decomposition. The program evaluates the…
The calculation of the two-loop corrections to the three jet production rate and to event shapes in electron-positron annihilation requires the computation of a number of up to now unknown two-loop four-point master integrals with one…
We present analytical results for one-loop five-point master integrals with up to three off-shell legs. The method of canonical differential equations along with the Simplified Differential Equations approach is employed. All necessary…
By the unitarity cut method, analytic expressions of one-loop coefficients have been given in spinor forms. In this paper, we present one-loop coefficients of various bases in Lorentz-invariant contraction forms of external momenta. Using…
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 calculate the three-loop master integrals contributing to the three-loop five-point amplitude on the special Coulomb branch of $\mathcal{N}=4$ SYM theory. For the genuine pentagon integrals, we follow the approach of Ref. [JHEP 12 (2025)…
Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We…
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…
The phase-integral method (PIM) is an asymptotic method of the geometrical optics or semi-classical type for solving approximately, but in many cases very accurately, a wide class of differential equations in physics. Unlike the related…
We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…
For loop integrals, the standard method is reduction. A well-known reduction method for one-loop integrals is the Passarino-Veltman reduction. Inspired by the recent paper [1] where the tadpole reduction coefficients have been solved, in…
To quantify degree of spatial inhomogeneity for multiphase materials we adapt the entropic descriptor (ED) of a pillar model developed to greyscale images. To uncover the contribution of each phase we introduce the suitable 'phase…
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…
We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these…
Integration by parts is used to reduce scalar Feynman integrals to master integrals.