Related papers: Progress in multiloop calculations
A new method is developed to calculate multiloop Feynman diagrams in non-relativistic field theories. A consistent scheme for regularizing and renormalizing loop integrals is established and shown to reproduce the results of dimensional…
This paper gives an overview from the perspective of Lie group theory of some of the recent advances in the rapidly expanding research area of quantum entanglement. This paper is a written version of the last of eight one hour lectures…
We review the method of the calculation of multiloop integrals recently suggested in Ref.[Lee2010]. A simple method of derivation of the dimensional recurrence relation suitable for automatization is given. Some new analytic results are…
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…
An asymptotic expansion of the two-loop two-point ``master'' diagram with two masses $m$ and $M$, on the mass shell $Q^2=M^2$, is presented. The treatment of the non-analytical terms arising in the expansion around the branching point is…
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of…
We present a method to evaluate numerically Feynman diagrams directly from their Feynman parameters representation. We first disentangle overlapping singularities using sector decomposition. Threshold singularities are treated with an…
A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different…
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This…
The success of the experimental program at the Tevatron re-inforced the idea that precision physics at hadron colliders is desirable and, indeed, possible. The Tevatron data strongly suggests that one-loop computations in QCD describe hard…
A brief review of recent results on asymptotic expansions of Feynman integrals on the mass shell in momenta and masses and their application to 2-loop calculations is presented.
The role of hyperlogarithms and multiple zeta values (and their generalizations) in Feynman amplitudes is being gradually recognized since the mid 1990's. The present lecture provides a concise introduction to a fast developing subject that…
In this talk I review the connections between Feynman integrals and multiple polylogarithms. After an introductory section on loop integrals I discuss the Mellin-Barnes transformation and shuffle algebras. In a subsequent section multiple…
This study is targeted to the NLO corrections of multileg processes, very important for the LHC. Starting from the construction of Feynman diagrams, the analytical reduction of general one-loop integrals to scalar master ones, the…
An explicit investigation about the equal-mass two-loop sunrise Feynman graph is performed. Such perturbative amplitude is related with many important physical process treated in the standard model context. The background of this…
In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and discuss introduce their…
We report on the progress in constructing contracted one-loop tensors. Analytic results for rank R=4 tensors, cross-checked numerically, are presented for the first time.
We propose a general coaction for families of integrals appearing in the evaluation of Feynman diagrams, such as multiple polylogarithms and generalized hypergeometric functions. We further conjecture a link between this coaction and…
For the calculation of multi-loop Feynman integrals, a novel numerical method, the Direct Computation Method (DCM) is developed. It is a combination of a numerical integration and a series extrapolation. In principle, DCM can handle…
We briefly review the technology involved in extracting the field-theory limit of multiloop bosonic string amplitudes, and we apply it to the evaluation of simple two-loop diagrams involving scalars and gauge bosons.