We describe a constructive procedure to separate overlapping infrared divergences in multiloop integrals. Working with a parametric representation in D = 4 − 2ǫ dimensions, adequate subtractions lead to a Laurent series in ǫ, where the coefficients of the pole-and finite terms are sums of regular parameter integrals which can be evaluated numerically. We fully automatized this algorithm by implementing it into algebraic manipulation programs and applied it to calculate numerically some nontrivial 2-loop 4-point and 3-loop 3-point Feynman diagrams. Finally, we discuss the applicability of our method to phenomenologically relevant multi-loop calculations such as the NNLO QCD corrections for e + e − → 3 jets.

We discuss the production of photon pairs in hadronic collisions, from fixed target to LHC energies. The study which follows is based on a QCD calculation at full next-to-leading order accuracy, including single and double fragmentation contributions, and implemented in the form of a general purpose computer program of "partonic event generator" type. To illustrate the possibilities of this code, we present the comparison with observables measured by the WA70 and D0 collaborations, and some predictions for the irreducible background to the search of Higgs bosons at LHC in the channel h → γγ. We also discuss theoretical scale uncertainties for these predictions, and examine several infrared sensitive situations which deserve further study.

We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which naturally isolates infrared divergences by construction. We prove that for N ≥ 5, higher dimensional integrals can be avoided. We derive many useful relations which allow for algebraic simplifications of one-loop amplitudes. We introduce a form factor representation of tensor integrals which contains no inverse Gram determinants by choosing a convenient set of basis integrals. For the evaluation of these basis integrals we propose two methods: An evaluation based on the analytical representation, which is fast and accurate away from exceptional kinematical configurations, and a robust numerical one, based on multi-dimensional contour deformation. The formalism can be implemented straightforwardly into a computer program to calculate next-to-leading order corrections to multi-particle processes in a largely automated way. E Hexagon relations from helicity decomposition 61 2

Physics at the Large Hadron Collider (LHC) and the International e + e − Linear Collider (ILC) will be complementary in many respects, as has been demonstrated at previous generations of hadron and lepton colliders. This report addresses the possible interplay between the LHC and ILC in testing the Standard Model and in discovering and determining the origin of new physics. Mutual benefits for the physics programme at both machines can occur both at the level of a combined interpretation of Hadron Collider and Linear Collider data and at the level of combined analyses of the data, where results obtained at one machine can directly influence the way analyses are carried out at the other machine. Topics under study comprise the physics of weak and strong electroweak symmetry breaking, supersymmetric models, new gauge theories, models with extra dimensions, and electroweak and QCD precision physics. The status of the work that has been carried out within the LHC / LC Study Group so far is summarised in this report. Possible topics for future studies are outlined.4

Pair production of W bosons constitutes an important background to Higgs boson and new physics searches at the Large Hadron Collider LHC. We have calculated the loop-induced gluon-fusion process gg → W * W * → leptons, including intermediate light and heavy quarks and allowing for arbitrary invariant masses of the W bosons. While formally of next-to-next-to-leading order, the gg → W * W * → leptons process is enhanced by the large gluon flux at the LHC and by experimental Higgs search cuts, and increases the next-to-leading order W W background estimate for Higgs searches by about 30%. We have extended our previous calculation to include the contribution from the intermediate topbottom massive quark loop and the Higgs signal process. We provide updated results for cross sections and differential distributions and study the interference between the different gluon scattering contributions. We describe important analytical and numerical aspects of our calculation and present the public GG2WW event generator.