463 research outputs found
On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case
We develop an algorithm of polynomial complexity for evaluating one-loop
amplitudes with an arbitrary number of external particles. The algorithm is
implemented in the Rocket program. Starting from particle vertices given by
Feynman rules, tree amplitudes are constructed using recursive relations. The
tree amplitudes are then used to build one-loop amplitudes using an integer
dimension on-shell cut method. As a first application we considered only three
and four gluon vertices calculating the pure gluonic one-loop amplitudes for
arbitrary external helicity or polarization states. We compare our numerical
results to analytical results in the literature, analyze the time behavior of
the algorithm and the accuracy of the results, and give explicit results for
fixed phase space points for up to twenty external gluons.Comment: 22 pages, 9 figures; v2: references added, version accepted for
publicatio
Testing and improving the numerical accuracy of the NLO predictions
I present a new and reliable method to test the numerical accuracy of NLO
calculations based on modern OPP/Generalized Unitarity techniques. A convenient
solution to rescue most of the detected numerically inaccurate points is also
proposed.Comment: References added. 1 Table added. Version accepted for publicatio
Optimizing the Reduction of One-Loop Amplitudes
We present an optimization of the reduction algorithm of one-loop amplitudes
in terms of master integrals. It is based on the exploitation of the polynomial
structure of the integrand when evaluated at values of the loop-momentum
fulfilling multiple cut-conditions, as emerged in the OPP-method. The
reconstruction of the polynomials, needed for the complete reduction, is rended
very versatile by using a projection-technique based on the Discrete Fourier
Transform. The novel implementation is applied in the context of the NLO QCD
corrections to u d-bar --> W+ W- W+
On the Rational Terms of the one-loop amplitudes
The various sources of Rational Terms contributing to the one-loop amplitudes
are critically discussed. We show that the terms originating from the generic
(n-4)-dimensional structure of the numerator of the one-loop amplitude can be
derived by using appropriate Feynman rules within a tree-like computation. For
the terms that originate from the reduction of the 4-dimensional part of the
numerator, we present two different strategies and explicit algorithms to
compute them.Comment: 14 pages, 3 figures, uses axodraw.st
NLO QCD calculations with HELAC-NLO
Achieving a precise description of multi-parton final states is crucial for
many analyses at LHC. In this contribution we review the main features of the
HELAC-NLO system for NLO QCD calculations. As a case study, NLO QCD corrections
for tt + 2 jet production at LHC are illustrated and discussed.Comment: 7 pages, 4 figures. Presented at 10th DESY Workshop on Elementary
Particle Theory: Loops and Legs in Quantum Field Theory, Worlitz, Germany,
April 25-30, 201
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
CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes
We present a program that implements the OPP reduction method to extract the
coefficients of the one-loop scalar integrals from a user defined
(sub)-amplitude or Feynman Diagram, as well as the rational terms coming from
the 4-dimensional part of the numerator. The rational pieces coming from the
epsilon-dimensional part of the numerator are treated as an external input, and
can be computed with the help of dedicated tree-level like Feynman rules.
Possible numerical instabilities are dealt with the help of arbitrary
precision routines, that activate only when needed.Comment: Version published in JHE
Feynman rules for the rational part of the Electroweak 1-loop amplitudes
We present the complete set of Feynman rules producing the rational terms of
kind R_2 needed to perform any 1-loop calculation in the Electroweak Standard
Model. Our results are given both in the 't Hooft-Veltman and in the Four
Dimensional Helicity regularization schemes. We also verified, by using both
the 't Hooft-Feynman gauge and the Background Field Method, a huge set of Ward
identities -up to 4-points- for the complete rational part of the Electroweak
amplitudes. This provides a stringent check of our results and, as a
by-product, an explicit test of the gauge invariance of the Four Dimensional
Helicity regularization scheme in the complete Standard Model at 1-loop. The
formulae presented in this paper provide the last missing piece for completely
automatizing, in the framework of the OPP method, the 1-loop calculations in
the SU(3) X SU(2) X U(1) Standard Model.Comment: Many thanks to Huasheng Shao for having recomputed, independently of
us, all of the effective vertices. Thanks to his help and by
comparing with an independent computation we performed in a general
gauge, we could fix, in the present version, the following formulae: the
vertex in Eq. (3.6), the vertex in Eq. (3.8),
Eqs (3.16), (3.17) and (3.18
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