On the tensor reduction of one-loop pentagons and hexagons

We perform analytical reductions of one-loop tensor integrals with 5 and 6 legs to scalar master integrals. They are based on the use of recurrence relations connecting integrals in different space-time dimensions. The reductions are expressed in a compact form in terms of signed minors, and have been implemented in a mathematica package called hexagon.m. We present several numerical examples.Comment: Latex, 7 pages, 2 eps figures. Contribution to the proceedings of `Loops and Legs in Quantum Field Theory', April 2008, Sondershausen, German

Feynman Rules for the Rational Part of the QCD 1-loop amplitudes

We compute the complete set of Feynman Rules producing the Rational Terms of kind R_2 needed to perform any QCD 1-loop calculation. We also explicitly check that in order to account for the entire R_2 contribution, even in case of processes with more than four external legs, only up to four-point vertices are needed. Our results are expressed both in the 't Hooft Veltman regularization scheme and in the Four Dimensional Helicity scheme, using explicit color configurations as well as the color connection language.Comment: 18 pages, 11 figures. Misprints corrected in Appendix A. Version to be published in JHE

Towards W b bbar + j at NLO with an automatized approach to one-loop computations

We present results for the O(alpha_s) virtual corrections to q g -> W b bbar q' obtained with a new automatized approach to the evaluation of one-loop amplitudes in terms of Feynman diagrams. Together with the O(alpha_s) corrections to q q' -> W b bbar g, which can be obtained from our results by crossing symmetry, this represents the bulk of the next-to-leading order virtual QCD corrections to W b bbar + j and W b + j hadronic production, calculated in a fixed-flavor scheme with four light flavors. Furthermore, these corrections represent a well defined and independent subset of the 1-loop amplitudes needed for the NNLO calculation of W b bbar. Our approach was tested against several existing results for NLO amplitudes including selected O(alpha_s) one-loop corrections to W + 3 j hadronic production. We discuss the efficiency of our method both with respect to evaluation time and numerical stability.Comment: 14 pages, 3 figure

Golem95C: A library for one-loop integrals with complex masses

We present a program for the numerical evaluation of scalar integrals and tensor form factors entering the calculation of one-loop amplitudes which supports the use of complex masses in the loop integrals. The program is built on an earlier version of the golem95 library, which performs the reduction to a certain set of basis integrals using a formalism where inverse Gram determinants can be avoided. It can be used to calculate one-loop amplitudes with arbitrary masses in an algebraic approach as well as in the context of a unitarity-inspired numerical reconstruction of the integrand.Comment: 22 pages, 3 figure

Multi-gluon one-loop amplitudes using tensor integrals

An efficient numerical algorithm to evaluate one-loop amplitudes using tensor integrals is presented. In particular, it is shown by explicit calculations that for ordered QCD amplitudes with a number of external legs up to 10, its performance is competitive with other methods.Comment: 25 pages, results for quark loops added, accuracy analysis extended, mistakes corrected, reference adde

Optimising Code Generation with haggies

This article describes haggies, a program for the generation of optimised programs for the efficient numerical evaluation of mathematical expressions. It uses a multivariate Horner-scheme and Common Subexpression Elimination to reduce the overall number of operations. The package can serve as a back-end for virtually any general purpose computer algebra program. Built-in type inference that allows to deal with non-standard data types in strongly typed languages and a very flexible, pattern-based output specification ensure that haggies can produce code for a large variety of programming languages. We currently use haggies as part of an automated package for the calculation of one-loop scattering amplitudes in quantum field theories. The examples in this articles, however, demonstrate that its use is not restricted to the field of high energy physics.Comment: 66 pages, 5 figures, program files for download at http://www.nikhef.nl/~thomasr

NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. full hadronic results

We present predictions for top anti-top bottom anti-bottom production at the LHC in next-to-leading order QCD. The precise description of this background process is a prerequisite to observe associated top anti-top Higgs production in the Higgs -> bottom anti-bottom decay channel and to directly measure the top-quark Yukawa coupling at the LHC. The leading-order cross section is extremely sensitive to scale variations. We observe that the traditional scale choice adopted in ATLAS simulations underestimates the top anti-top bottom anti-bottom background by a factor two and introduce a new dynamical scale that stabilizes the perturbative predictions. We study various kinematic distributions and observe that the corrections have little impact on their shapes if standard cuts are applied. In the regime of highly boosted Higgs bosons, which offers better perspectives to observe the top anti-top Higgs signal, we find significant distortions of the kinematic distributions. The one-loop amplitudes are computed using process-independent algebraic manipulations of Feynman diagrams and numerical tensor reduction. We find that this approach provides very high numerical stability and CPU efficiency.Comment: 42 pages, LaTeX, 44 postscript figure

A FORTRAN code for γγ→ZZ\gamma \gamma \to Z Z in SM and MSSM

Through the present paper, the code gamgamZZ is presented, which may be used to calculate all possible observables related to the process $\gamma \gamma \to ZZ$, in either the Standard Model (SM), or the minimal sypersymmetric standard model (MSSM) with real parameters.Comment: 13 pages, 7 figures Revised according to the EPJC Referee suggestion

Reduction Method for One-loop Tensor 5- and 6-point Integrals Revisited.

A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for the cancellation of leading inverse Gram determinants.The resulting compact formulae allow both for a study of analytical properties and for efficient numerical programming. Here some special numerical examples are presented.Comment: Prepared for 2008 International Linear Collider Workshop (LCWS08 and ILC08), Chicago, 16-20 Nov. 200