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Sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory. We explain the general algorithm in detail and review its application to multi-loop Feynman parameter integrals as well as infrared divergent phase-space integrals over real radiation matrix elements.
We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional external momenta to box integrals in (4 − 2ǫ) dimensions. We derive a formula valid for arbitrary N and give an explicit… (More)
We complete the calculation of master integrals for massless three-loop form factors by computing the previously-unknown three diagrams with nine propagators in dimensional regularisation. Each of the integrals yields a six-fold Mellin-Barnes representation which we use to compute the coefficients of the Laurent expansion in ǫ. Using Riemann ζ functions of… (More)
We derive the six-photon scattering amplitudes for all helicity configurations, obtaining compact analytical expressions. Two recently developed methods, based on form factor decomposition and on multiple cuts are used for this calculation. The self-interaction of photons (light-by-light scattering) mediated through a virtual charged fermion loop is a… (More)
The method of Mellin–Barnes representation is used to calculate dimensionally regularized massive on-shell double box Feynman diagrams contributing to Bhabha scattering at two loops.
We present numerical results for massive non-planar two-loop box integrals entering heavy quark pair production at NNLO, some of which are not known analytically yet. The results have been obtained with the program SecDec 2.1, based on sector decomposition and contour deformation, in combination with new types of transformations. Among the new features of… (More)
The inclusive four-particle phase space integral of any 1 → 4 matrix element in massless QCD contains divergences due to the soft and collinear emission of up to two particles in the final state. We show that any term appearing in this phase space integral can be expressed as linear combination of only four master integrals. These four master integrals are… (More)
We compute production rates for two, three, four, and five jets in electron-positron annihilation at the third order in the QCD coupling constant. At this order, three-jet production is described to next-to-next-to-leading order in perturbation theory while the two-jet rate is obtained at next-to-next-to-next-to-leading order. Our results yield an improved… (More)