Six-Photon Amplitudes

We present analytical results for all six-photon helicity amplitudes. For the computation of this loop induced process two recently developed methods, based on form factor decomposition and on multiple cuts, have been used. We obtain compact results, demonstrating the applicability of both methods to one-loop amplitudes relevant to precision collider phenomenology.Comment: replaced by published versio

Towards LHC phenomenology at the loop level: A new method for one-loop amplitudes

A precise understanding of LHC phenomenology requires the inclusion of one-loop corrections for multi-particle final states. In this talk we describe a semi-numerical method to compute one-loop amplitudes with many external particles and present first applications.Comment: 5 pages latex, 1 ps fig., 1 eps fig., Conference Proceedings Radcor 200

Analytic Results for Massless Three-Loop Form Factors

We evaluate, exactly in d, the master integrals contributing to massless three-loop QCD form factors. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm. Using our results for the master integrals we obtain analytical expressions for two missing constants in the ep-expansion of the two most complicated master integrals and present the form factors in a completely analytic form.Comment: minor revisions, to appear in JHE

A general reduction method for one-loop N-point integrals

In order to calculate cross sections with a large number of particles/jets in the final state at next-to-leading order, one has to reduce the occurring scalar and tensor one-loop integrals to a small set of known integrals. In massless theories, this reduction procedure is complicated by the presence of infrared divergences. Working in n=4-2*epsilon dimensions, it will be outlined how to achieve such a reduction for diagrams with an arbitrary number of external legs. As a result, any integral with more than four propagators and generic 4-dimensional external momenta can be reduced to box integrals.Comment: 5 pages Latex, 1 eps figure included, uses npb.sty (included). Talk presented at the conference: Loops and Legs in Quantum Field Theory, April 2000, Bastei, German

Next-to-leading order multi-leg processes for the Large Hadron Collider

In this talk we discuss recent progress concerning precise predictions for the LHC. We give a status report of three applications of our method to deal with multi-leg one-loop amplitudes: The interference term of Higgs production by gluon- and weak boson fusion to order O(alpha^2 alpha_s^3) and the next-to-leading order corrections to the two processes pp -> ZZ jet and u ubar -> d dbar s sbar. The latter is a subprocess of the four jet cross section at the LHC.Comment: 6 pages, 5 figures. Talk given at the 8th international Symposium on Radiative Corrections (RADCOR), October 1-5 2007, Florence, Ital

Numerical evaluation of multi-loop integrals by sector decomposition

In a recent paper we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines. Here we show how to extend this algorithm to Feynman diagrams with massive propagators and arbitrary propagator powers. As applications, we present numerical results for the master 2-loop 4-point topologies with massive internal lines occurring in Bhabha scattering at two loops, and for the master integrals of planar and non-planar massless double box graphs with two off-shell legs. We also evaluate numerically some two-point functions up to 5 loops relevant for beta-function calculations, and a 3-loop 4-point function, the massless on-shell planar triple box. Whereas the 4-point functions are evaluated in non-physical kinematic regions, the results for the propagator functions are valid for arbitrary kinematics.Comment: 15 pages latex, 11 eps figures include

Numerical evaluation of phase space integrals by sector decomposition

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 emission part of the e+e- -> 2 jets cross section at NNLO. The explicit cancellation of infrared poles upon summation over all possible cuts of a given topology is worked out in detail for a specific example.Comment: 15 pages, 2 figure

Tensorial Reconstruction at the Integrand Level

We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the integration momentum. There are several interesting applications of this novel method within existing techniques for the reduction of one-loop multi-leg amplitudes: to deal with numerically unstable points, such as in the vicinity of a vanishing Gram determinant; to allow for a sampling of the numerator function based on real values of the integration momentum; to optimize the numerical reduction in the case of long expressions for the numerator functions.Comment: 20 pages, 2 figure

Calculation of 1-loop Hexagon Amplitudes in the Yukawa Model

We calculate a class of one-loop six-point amplitudes in the Yukawa model. The construction of multi-particle amplitudes is done in the string inspired formalism and compared to the Feynman diagrammatic approach. We show that there exists a surprisingly efficient way of calculating such amplitudes by using cyclic identities of kinematic coefficients and discuss in detail cancellation mechanisms of spurious terms. A collection of formulas which are useful for the calculation of massless hexagon amplitudes is given.Comment: 15 pages Late