Related papers: Two-loop three-point diagrams with irreducible num…
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…
Small momentum expansion of the "sunset" diagram with three different masses is obtained. Coefficients at powers of $p^2$ are evaluated explicitly in terms of dilogarithms and elementary functions. Also some power expansions of "sunset"…
In this paper we consider multi-loop integrals appearing in MHV scattering amplitudes of planar N=4 SYM. Through particular differential operators which reduce the loop order by one, we present explicit equations for the two-loop…
In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $\epsilon$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up…
Recently, algorithms for calculation of 3-loop propagator diagrams in HQET and on-shell QCD with a heavy quark have been constructed and implemented. These algorithms (based on integration by parts recurrence relations) reduce an arbitrary…
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 the complete set of planar master integrals relevant to the calculation of three-point functions in four-loop massless Quantum Chromodynamics. Employing direct parametric integrations for a basis of finite integrals, we give…
In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…
We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of…
We present an extension of the renormalisation procedure based on the R-operation in $D$ dimensions at two-loop level, in which the numerators of all Feynman diagrams can be constructed in four dimensions, and the rational terms stemming…
We present a systematic method to determine the dominant regions of internal momenta contributing to any two-body high-energy near-forward scattering diagram. Such a knowledge is used to evaluate leading high-energy dependences of loop…
Work is reported on finite integral representations for 2-loop massive 2-, 3- and 4-point functions, using orthogonal and parallel space variables. It is shown that this can be utilized to cover particles with arbitrary spin (tensor…
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…
We study tridimensional tensors on the complex field from the point of view of hypermatrices, taking into consideration the problem of determining whether they are degenerate or not, concise or not, what is their essential format if they…
Explicit expressions are considered for the generating functions concerning the number of planar diagrams with given numbers of 3- and 4-point vertices. It is observed that planar renormalization theory requires diagrams with restrictions,…
In this paper we initiate the study of tropical Voronoi diagrams. We start out with investigating bisectors of finitely many points with respect to arbitrary polyhedral norms. For this more general scenario we show that bisectors of three…
We give an algorithm for obtaining expansions of massive two-loop Feynman graphs in powers of the external momentum around a finite, nonzero value of the momentum. This is based on our general two-loop formalism to reduce massive two-loop…
An algorithm for calculation of three-loop propagator diagrams in HQET, based on integration-by-parts recurrence relations, is constructed and implemented as a REDUCE package Grinder, and in Axiom.
In this paper we study for the incompressible Euler equations the global structure of the bifurcation diagram for the rotating doubly connected patches near the degenerate case. We show that the branches with the same symmetry merge forming…
We present an analytic calculation of three-loop four-point Feynman integrals with two off-shell legs of equal mass. We provide solutions to the canonical differential equations of two integral families in both Euclidean and physical…