Related papers: Evaluating single-scale and/or non-planar diagrams…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha \alpha_s$ corrections…
The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…
We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…
We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential…
It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
General prescriptions for evaluation of coefficients at arbitrary powers and logarithms in the asymptotic expansion of Feynman diagrams in the Sudakov limit are discussed and illustrated by two-loop examples. Peculiarities connected with…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then,…
We propose a strategy to study the analytic structure of Feynman parameter integrals where singularities of the integrand consist of rational irreducible components. At the core of this strategy is the identification of a selected stratum…
We present analytic results for all the Feynman integrals relevant for ${\mathcal O}(\alpha \alpha_s)$ virtual corrections to $H \rightarrow ZZ^*$ decay. We use the method of differential equations to solve the master integrals while…
We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter $x$ and the dimension $d$, in the whole kinematic range of $x$. The method is based on differential equations, which, however, do not…
The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the…
Stable reduction methods will be important in the evaluation of high-order perturbative diagrams appearing in QCD and mixed QCD-electroweak radiative corrections at the LHC. Differential reduction techniques are useful for relating…
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…
We review an approach for the computation of Feynman integrals by use of multiple polylogarithms, with an emphasis on the related criterion of linear reducibility of the graph. We show that the set of graphs which satisfies the linear…
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
We compute three families of two-loop six-point massless Feynman integrals in dimensional regularization, namely the double-box, the pentagon-triangle, and the hegaxon-bubble family. This constitutes the first analytic computation of…
I study the Feynman integrals needed to compute two-loop self-energy functions for general masses and external momenta. A convenient basis for these functions consists of the four integrals obtained at the end of Tarasov's recurrence…