Related papers: Numerical evaluation of phase space integrals by s…
It is described how the method of sector decomposition can serve to disentangle overlapping infrared singularities, in particular those occurring in the calculation of the real emission part of e+e- to 2 jets and e+e- to 3 jets at NNLO.
A method based on sector decomposition is briefly described which is suitable for the calculation of the double real radiation part of e^+e^- to 3 jets at next-to-next-to-leading order in a fully differential way.
A method based on sector decomposition has been developed to calculate the double real radiation part of the process e+e- to 3 jets at next-to-next-to-leading order. It is shown in an example that the numerical cancellation of soft and…
We report on the sector decomposition approach to the double real radiation part of e^+e^- to 3 jets at NNLO.
I review the state-of-the-art for fully differential numerical NNLO programs. Topics which are covered include the calculation of two-loop amplitudes, multiple polylogarithms, cancellation of infra-red divergences at NNLO and the efficient…
We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon,…
Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are…
Detailed description of the calculation of the 2-loop self-energy for a scalar particle is presented. By employing a simple sector decomposition method, the ultraviolet divergent part is efficiently separated from the finite part. The…
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 previous articles we outlined a subtraction scheme for regularizing doubly-real emission and real-virtual emission in next-to-next-to-leading order (NNLO) calculations of jet cross sections in electron-positron annihilation. In order to…
We propose a new method of computing real emission contributions to hard QCD processes. Our approach uses sector decomposition of the exclusive final-state phase space to enable extraction of all singularities of the real emission matrix…
Sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory. We explain the general algorithm in detail and review its application to multi-loop Feynman…
One-loop integrands can be written in terms of a simple, process-independent basis. We show that a similar basis exists for integrands of phase-space integrals for the real-emission contribution at next-to-leading order. Our demonstration…
A non-iterative method is presented for the factorization step of sector decomposition method, which separates infrared divergent part from loop integration. This method is based on a classification of asymptotic behavior of polynomials.…
The inclusive four-particle phase space integral of any $1\to 4$ matrix element in massless QCD contains divergences due to the soft and collinear emission of up to two particles in the final state. We show that any term appearing in this…
We briefly review numerical methods for calculations beyond one loop and then describe new developments within the method of sector decomposition in more detail. We also discuss applications to two-loop integrals involving several mass…
The computation of Feynman integrals is often the bottleneck of multi-loop calculations. We propose and implement a new method to efficiently evaluate such integrals in the physical region through the numerical integration of a suitable set…
In this talk we discuss sector decomposition. This is a method to disentangle overlapping singularities through a sequence of blow-ups. We report on an open-source implementation of this algorithm to compute numerically the Laurent…
We discuss an algorithm for the numerical evaluation of NLO multiparton processes. We focus hereby on the virtual part of the NLO calculation, i.e. on evaluating the one-loop integration numerically. We employ and extend the ideas of the…
So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of…