23 research outputs found
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 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 , 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