Related papers: Numerical integration of loop integrals through lo…
We propose a method for computing numerically integrals defined via $i \epsilon$ deformations acting on single-pole singularities. We achieve this without an explicit analytic contour deformation. Our solution is then used to produce…
The loop-tree duality (LTD) has become a novelty alternative to bootstrap the numerical evaluation of multi-loop scattering amplitudes. It has indeed been found that Feynman integrands, after the application of LTD, display a representation…
Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…
We review the recent developments of the Loop-Tree Duality method, focussing our discussion on the first numerical implementation and its use in the direct numerical computation of multi-leg Feynman integrals. Non-trivial examples are…
We present a local subtraction scheme that enables the combined integration of loop momenta and the final-state parton phase space in real-virtual NNLO QCD corrections to cross sections for hadroproduction of electroweak and other colorless…
We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the…
This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…
Using loop-tree duality, we relate a renormalised $n$-point $l$-loop amplitude in a quantum field theory to a phase-space integral of a regularised $l$-fold forward limit of a UV-subtracted $(n+2l)$-point tree-amplitude-like object. We show…
We introduce a streamlined method for evaluating in-in loop integrals using dimensional regularization for diagrams with an arbitrary number of external legs and vertices, which complements earlier work and facilitates the extraction of the…
We report our experiences with the generalized integration-by-parts algorithm [hep-ph/9609429] in the context of calculations of a realistic one-loop subset of diagrams.
We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…
We calculate the two-loop vertex function for the crossed topology, and for arbitrary masses and external momenta. We derive a double integral representation, suitable for a numerical evaluation by a Gaussian quadrature. Real and imaginary…
We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The…
The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over an Euclidean space. In this article, we review the last developments concerning…
We propose a new method to calculate the 4-dimensional divergent integrals. By calculating the one loop integral as an example, the regularization of the integrals in 3-dimension momentum space are given in details. We find that the new…
The spinor-helicity formalism has proven to be very efficient in the calculation of scattering amplitudes in quantum field theory, while the loop tree duality (LTD) representation of multi-loop integrals exhibits appealing and interesting…
We discuss briefly the first numerical implementation of the Loop-Tree Duality (LTD) method. We apply the LTD method in order to calculate ultraviolet and infrared finite multi-leg one-loop Feynman integrals. We attack scalar and tensor…
The unitarity method for calculating one-loop amplitudes provides algorithms of polynomial complexity. This is primarily beneficial for the computation of multi-leg one loop amplitudes and it is therefore of great interest to develop a…
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…
Multi-loop scattering amplitudes constitute a serious bottleneck in current high-energy physics computations. Obtaining new integrand level representations with smooth behaviour is crucial for solving this issue, and surpassing the…