Numerical Computation of Two-loop Box Diagrams with Masses

A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass configurations. As an example, the computation of two-loop planar and non-planar box diagrams is shown. The results are confirmed by comparisons with other techniques, including the reduction method, and by a consistency check using the dispersion relation.Comment: 16 pages, 8 figure

The Cut-Constructible Part of QCD Amplitudes

Unitarity cuts are widely used in analytic computation of loop amplitudes in gauge theories such as QCD. We expand upon the technique introduced in hep-ph/0503132 to carry out any finite unitarity cut integral. This technique naturally separates the contributions of bubble, triangle and box integrals in one-loop amplitudes and is not constrained to any particular helicity configurations. Loop momentum integration is reduced to a sequence of algebraic operations. We discuss the extraction of the residues at higher-order poles. Additionally, we offer concise algebraic formulas for expressing coefficients of three-mass triangle integrals. As an application, we compute all remaining coefficients of bubble and triangle integrals for nonsupersymmetric six-gluon amplitudes.Comment: 78 pages, 3 fig

Automating methods to improve precision in Monte-Carlo event generation for particle colliders

This thesis concerns with numerical methods for a theoretical description of high energy particle scattering experiments. It focuses on fixed order perturbative calculations, i.e. on matrix elements and scattering cross sections at leading and next-to-leading order. For the leading order a number of algorithms for the matrix element generation and the numeric integration over the phase space are studied and implemented in a computer code, which allows to push the current limits on the complexity of the final state and the precision. For next-to-leading order calculations necessary steps towards a fully automated treatment are performed. A subtraction method that allows a process independent regularization of the divergent virtual and real corrections is implemented, and a new approach for a semi-numerically evaluation of one-loop amplitudes is investigated