15 research outputs found
One-loop amplitudes for W+3 jet production in hadron collisions
We employ the recently developed method of generalized -dimensional
unitarity to compute one-loop virtual corrections to all scattering amplitudes
relevant for the production of a boson in association with three jets in
hadronic collisions, treating all quarks as massless.Comment: 26 pages, 5 figures, v2 to agree with published versio
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
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
On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
A closed formula is obtained for the infrared singularities of dimensionally
regularized, massless gauge-theory scattering amplitudes with an arbitrary
number of legs and loops. It follows from an all-order conjecture for the
anomalous-dimension matrix of n-jet operators in soft-collinear effective
theory. We show that the form of this anomalous dimension is severely
constrained by soft-collinear factorization, non-abelian exponentiation, and
the behavior of amplitudes in collinear limits. Using a diagrammatic analysis,
we demonstrate that these constraints imply that to three-loop order the
anomalous dimension involves only two-parton correlations, with the possible
exception of a single color structure multiplying a function of conformal cross
ratios depending on the momenta of four external partons, which would have to
vanish in all two-particle collinear limits. We argue that such a function does
not appear at three-loop order, and that the same is true in higher orders. Our
formula predicts Casimir scaling of the cusp anomalous dimension to all orders
in perturbation theory, and we explicitly check that the constraints exclude
the appearance of higher Casimir invariants at four loops. Using known results
for the quark and gluon form factors, we derive the three-loop coefficients of
the 1/epsilon^n pole terms (with n=1,...,6) for an arbitrary n-parton
scattering amplitude in massless QCD. This generalizes Catani's two-loop
formula proposed in 1998.Comment: 46 pages, 9 figures; v2: improved treatment of collinear limits,
references added; v3: improved discussion of non-abelian exponentiation,
references updated; v4: typo in eq. (17) fixed, references updated; v5:
additional term in (17
Generalized unitarity at work: first NLO QCD results for hadronic W+3jet production
We compute the leading color, next-to-leading order QCD corrections to the
dominant partonic channels for the production of a W boson in association with
three jets at the Tevatron and the LHC. This is the first application of
generalized unitarity for realistic one-loop calculations. The method performs
well in this non-trivial test and offers great promise for the future.Comment: 20 pages, 4 figure
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
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+
Polarizing the Dipoles
We extend the massless dipole formalism of Catani and Seymour, as well as its
massive version as developed by Catani, Dittmaier, Seymour and Trocsanyi, to
arbitrary helicity eigenstates of the external partons. We modify the real
radiation subtraction terms only, the primary aim being an improved efficiency
of the numerical Monte Carlo integration of this contribution as part of a
complete next-to-leading order calculation. In consequence, our extension is
only applicable to unpolarized scattering. Upon summation over the helicities
of the emitter pairs, our formulae trivially reduce to their original form. We
implement our extension within the framework of Helac-Phegas, and give some
examples of results pertinent to recent studies of backgrounds for the LHC. The
code is publicly available. Since the integrated dipole contributions do not
require any modifications, we do not discuss them, but they are implemented in
the software.Comment: 20 pages, 4 figures, Integrated dipoles implemented for massless and
massive case
Automated one-loop calculations: a proof of concept
An algorithm, based on the OPP reduction method, to automatically compute any
one-loop amplitude, for all momentum, color and helicity configurations of the
external particles, is presented. It has been implemented using the tree-order
matrix element code HELAC and the OPP reduction code CutTools. As a
demonstration of the potential of the current implementation, results for all
sub-processes included in the 2007 Les Houches wish list for LHC, are
presented.Comment: 22 pages, published versio
Direct Extraction Of One Loop Rational Terms
We present a method for the direct extraction of rational contributions to
one-loop scattering amplitudes, missed by standard four-dimensional unitarity
techniques. We use generalised unitarity in D=4-2\e dimensions to write the
loop amplitudes in terms of products of massive tree amplitudes. We find that
the rational terms in 4-2\e dimensions can be determined from quadruple,
triple and double cuts without the need for independent pentagon contributions
using a massive integral basis. The additional mass-dependent integral
coefficients may then be extracted from the large mass limit which can be
performed analytically or numerically. We check the method by computing the
rational parts of all gluon helicity amplitudes with up to six external legs.
We also present a simple application to amplitudes with external massless
fermions.Comment: 35 pages, 6 figures. Major revisions: new analytic results for gluon
amplitudes and new section on treatment of massless fermions. References
added and typos corrected. Accepted for publication in JHE