Related papers: Reduction of one-loop n-point integrals
We present an optimization of the reduction algorithm of one-loop amplitudes in terms of master integrals. It is based on the exploitation of the polynomial structure of the integrand when evaluated at values of the loop-momentum fulfilling…
In order to meet the precision requirements for the LHC and future colliders, next-to-next-to-leading order corrections to a wide range of processes are essential, making general automated tools highly desirable. Extending the strategy of…
The superconformal Ward identities combined with N=2 harmonic analyticity are used to evaluate two-loop four-point correlation functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory in terms of the well-known…
We suggest a possible algorithm to calculate one-loop n-point functions within a variant of light-front perturbation theory. The key ingredients are the covariant Passarino-Veltman scheme and a surprising integration formula that localises…
Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction…
The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try…
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…
Finding relative pose between two calibrated images is a fundamental task in computer vision. Given five point correspondences, the classical five-point methods can be used to calculate the essential matrix efficiently. For the case of $N$…
We obtain all planar four-point correlators of half-BPS operators in $\mathcal{N}=4$ SYM up to five loops. The ansatz for the integrand is fixed partially by imposing light-cone OPE relations between different correlators. We then fix the…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
We propose a new set of Master Integrals which can be used as a basis for certain multiloop calculations in massless gauge field theories. In these theories we consider three-point Feynman diagrams with arbitrary number of loops. The…
We use the recently developed generalized double-copy procedure to construct an integrand for the five-loop four-point amplitude of N=8 supergravity. This construction starts from a naive double copy of the previously computed corresponding…
We introduce the fortran-library COLLIER for the numerical evaluation of one-loop scalar and tensor integrals in perturbative relativistic quantum field theories. Important features are the implementation of dedicated methods to achieve…
We present an approach to higher point loop integrals using Chinese magic in the virtual loop integration variable. We show, using the five point function in the important e^+e^-\to f\bar{f}+\gamma process for ISR as a pedagogical vehicle,…
We consider one-loop five-point QCD amplitudes in next-to-multi-Regge kinematics, and evaluate the one-loop impact factor for the emission of two gluons. This is the last ingredient which is necessary to evaluate the gluon-jet impact factor…
We present a semi-numerical method to compute one-loop corrections to processes involving many particles. We treat in detail cases with up to five external legs and massless internal propagators, although the method is more general.
We propose a new method for the computation of quantum three-point functions for operators in su(2) sectors of N=4 super Yang-Mills theory. The method is based on the existence of a unitary transformation relating inhomogeneous and…
We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…
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 present master formulas for the divergent part of the one-loop effective action for an arbitrary (both minimal and nonminimal) operators of any order in the 4-dimensional curved space. They can be considered as computer algorithms,…