Related papers: Resolution of singularities for multi-loop integra…
In a series of papers we have developed the method of iterated sector decomposition for the calculation of infrared divergent multi-loop integrals. Here we apply it to phase space integrals to calculate a contribution to the double real…
We present an algorithm of the reduction of the differential equations for master integrals the Fuchsian form with the right-hand side matrix linearly depending on dimensional regularization parameter $\epsilon$. We consider linear…
Nowadays the sector decomposition technique, which can isolate divergences from parametric representations of integrals, becomes a quite useful tool for numerical evaluations of the Feynman loop integrals. It is used to verify the…
We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general…
We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour…
We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…
At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one-loop, as further progress was hampered so far by the greater computational…
We propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with…
We describe in some detail the present features of an automatic loop calculation program as well as the integration techniques that go into it. The program, called XLOOPS 1.0, allows one to calculate massive one- and two-loop Feynman…
We give numerical integration results for Feynman loop diagrams such as those covered by Laporta [1] and by Baikov and Chetyrkin [2], and which may give rise to loop integrals with UV singularities. We explore automatic adaptive integration…
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…
In this paper, we propose a numerical method for computing Hadamard finite-part integrals with an integral-power singularity at an endpoint, the part of the divergent integral which is finite as a limiting procedure. In the proposed method,…
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two…
The problem of detecting of information and logically independent (DILD) steps in programs is a key for equivalent program transformations. Here we are considering the problem of independence of loop iterations, the concentration of massive…
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…
Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…
A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…
We present a semi-numerical algorithm to calculate one-loop virtual corrections to scattering amplitudes. The divergences of the loop amplitudes are regulated using dimensional regularization. We treat in detail the case of amplitudes with…
Two program packages are presented for evaluating one-loop amplitudes. They can work either in dimensional regularization or in constrained differential renormalization. The latter method is found at the one-loop level to be equivalent to…