Automatic Integral Reduction for Higher Order Perturbative Calculations

We present a program for the reduction of large systems of integrals to master integrals. The algorithm was first proposed by Laporta; in this paper, we implement it in MAPLE. We also develop two new features which keep the size of intermediate expressions relatively small throughout the calculation. The program requires modest input information from the user and can be used for generic calculations in perturbation theory.Comment: 23 page

Progress in NNLO calculations for scattering processes

The various motivations for improving the perturbative prediction to next-to-next-to-leading order (NNLO) for basic scattering processes in proton-(anti)proton, electron-proton and electron-positron scattering are discussed in detail. Recent progress in the field of next-to-next-to-leading order calculations is reviewed.Comment: Latex 9 pages, 2 postscript embedded figures, JHEP class, Based on invited talks at 6th International Symposium on Radiative Corrections, Application of Quantum Field Theory to Phenomenology (RADCOR 2002) and 6th Zeuthen Workshop on Elementary Particle Theory (Loops and Legs in Quantum Field Theory) Kloster Banz, Germany, 8th - 13th Sep 2002 and 14th Topical Conference on Hadron Collider Physics (HCP 2002), Karlsruhe, Germany, 29th Sep - 4th Oct 200

The Leading Power Regge Asymptotic Behaviour of Dimensionally Regularized Massless On-Shell Planar Triple Box

The leading power asymptotic behaviour of the dimensionally regularized massless on-shell planar triple box diagram in the Regge limit t/s -> 0 is analytically evaluated.Comment: 9 pages, LaTeX with axodraw.st

Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically

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 appropriate contour deformation. We have validated our technique comparing with recent analytic results for the gg->h two-loop amplitudes with heavy quarks and scalar quarks.Comment: 8 pages, 3 figures; references added, version to appear in JHE

The two-loop scalar and tensor pentabox graph with light-like legs

We study the scalar and tensor integrals associated with the pentabox topology: the class of two-loop box integrals with seven propagators - five in one loop and three in the other. We focus on the case where the external legs are light-like and use integration-by-parts identities to express the scalar integral in terms of two master-topology integrals and present an explicit analytic expression for the pentabox scalar integral as a series expansion in ep = (4-D)/2. We also give an algorithm based on integration by parts for relating the generic tensor integrals to the same two master integrals and provide general formulae describing the master integrals in arbitrary dimension and with general powers of propagators.Comment: Detailed expansions of intermediate results adde

Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box

The dimensionally regularized master planar double box Feynman diagram with four massive and three massless lines, powers of propagators equal to one, all four legs on the mass shell, i.e. with p_i^2=m^2, i=1,2,3,4, is analytically evaluated for general values of m^2 and the Mandelstam variables s and t. An explicit result is expressed in terms of polylogarithms, up to the third order, depending on special combinations of m^2,s and t.Comment: 10 pages, LaTeX with axodraw.st

Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off Shell

The dimensionally regularized massless non-planar double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with p_1^2=q^2\neq 0, and three legs on shell, p_i^2=0, i=2,3,4, is analytically calculated for general values of q^2 and the Mandelstam variables s,t and u (not necessarily restricted by the physical condition s+t+u=q^2). An explicit result is expressed through (generalized) polylogarithms, up to the fourth order, dependent on rational combinations of q^2,s,t and u, and simple finite two- and three fold Mellin--Barnes integrals of products of gamma functions which are easily numerically evaluated for arbitrary non-zero values of the arguments.Comment: 9 pages, LaTeX with axodraw.sty, minor changes in references, to appear in Physics Letters

Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box

The dimensionally regularized massless on-shell planar triple box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t in a Laurent expansion in the parameter \ep=(4-d)/2 of dimensional regularization up to a finite part. An explicit result is expressed in terms of harmonic polylogarithms, with parameters 0 and 1, up to the sixth order. The evaluation is based on the method of Feynman parameters and multiple Mellin-Barnes representation. The same technique can be quite similarly applied to planar triple boxes with any numerators and integer powers of the propagators.Comment: 8 pages, LaTeX with axodraw.st

Scattering amplitudes for e^+e^- --> 3 jets at next-to-next-to-leading order QCD

We present the calculation of the fermionic contribution to the QCD two-loop amplitude for e^+e^- --> q qbar g.Comment: 5 pages, 4 figures, espcrc2.sty (included), Talk given at QCD '02, Montpellier, France, 2-9th July 200

Analytic Continuation of Massless Two-Loop Four-Point Functions

We describe the analytic continuation of two-loop four-point functions with one off-shell external leg and internal massless propagators from the Euclidean region of space-like $1\to 3$ decay to Minkowskian regions relevant to all $1\to 3$ and $2\to 2$ reactions with one space-like or time-like off-shell external leg. Our results can be used to derive two-loop master integrals and unrenormalized matrix elements for hadronic vector-boson-plus-jet production and deep inelastic two-plus-one-jet production, from results previously obtained for three-jet production in electron--positron annihilation.Comment: 26 pages, LaTe