8,414 research outputs found
The rational parts of one-loop QCD amplitudes I: The general formalism
A general formalism for computing only the rational parts of oneloop QCD
amplitudes is developed. Starting from the Feynman integral representation of
the one-loop amplitude, we use tensor reduction and recursive relations to
compute the rational parts directly. Explicit formulas for the rational parts
are given for all bubble and triangle integrals. Formulas are also given for
box integrals up to two-masshard boxes which are the needed ingredients to
compute up to 6-gluon QCD amplitudes. We use this method to compute explicitly
the rational parts of the 5- and 6-gluon QCD amplitudes in two accompanying
papers.Comment: 49 pages, 8 figure and LaTeX file; minor corrections, references
added, to be published in Nucl. Phys.
Bootstrapping One-Loop QCD Amplitudes
We review the recently developed bootstrap method for the computation of
high-multiplicity QCD amplitudes at one loop. We illustrate the general
algorithm step by step with a six-point example. The method combines
(generalized) unitarity with on-shell recursion relations to determine the not
cut-constructible, rational terms of these amplitudes. Our bootstrap approach
works for arbitrary configurations of gluon helicities and arbitrary numbers of
external legs.Comment: 18 pages, 9 figures; extended version of talks given at the 7th
Workshop On Continuous Advances In QCD, 11-14 May 2006, Minneapolis,
Minnesota; at SUSY06: 14th International Conference On Supersymmetry And The
Unification Of Fundamental Interactions, 12-17 Jun 2006, Irvine, California;
at the LoopFest V: Radiative Corrections For The International Linear
Collider: Multi-Loops And Multi-Legs, 19-21 Jun 2006, SLAC, Menlo Park,
California; and at the Vancouver Linear Colliders Workshop (ALCPG 2006),
19-22 Jul 2006, Vancouver, British Columbi
Bootstrapping Multi-Parton Loop Amplitudes in QCD
We present a new method for computing complete one-loop amplitudes, including
their rational parts, in non-supersymmetric gauge theory. This method merges
the unitarity method with on-shell recursion relations. It systematizes a
unitarity-factorization bootstrap approach previously applied by the authors to
the one-loop amplitudes required for next-to-leading order QCD corrections to
the processes e^+e^- -> Z,\gamma^* -> 4 jets and pp -> W + 2 jets. We
illustrate the method by reproducing the one-loop color-ordered five-gluon
helicity amplitudes in QCD that interfere with the tree amplitude, namely
A_{5;1}(1^-,2^-,3^+,4^+,5^+) and A_{5;1}(1^-,2^+,3^-,4^+,5^+). Then we describe
the construction of the six- and seven-gluon amplitudes with two adjacent
negative-helicity gluons, A_{6;1}(1^-,2^-,3^+,4^+,5^+,6^+) and
A_{7;1}(1^-,2^-,3^+,4^+,5^+,6^+,7^+), which uses the previously-computed
logarithmic parts of the amplitudes as input. We present a compact expression
for the six-gluon amplitude. No loop integrals are required to obtain the
rational parts.Comment: 43 pages, 8 figures, RevTeX, v2-v4 clarifications and minor
correction
Bootstrapping One-Loop QCD Amplitudes with General Helicities
The recently developed on-shell bootstrap for computing one-loop amplitudes
in non-supersymmetric theories such as QCD combines the unitarity method with
loop-level on-shell recursion. For generic helicity configurations, the
recursion relations may involve undetermined contributions from non-standard
complex singularities or from large values of the shift parameter. Here we
develop a strategy for sidestepping difficulties through use of pairs of
recursion relations. To illustrate the strategy, we present sets of recursion
relations needed for obtaining n-gluon amplitudes in QCD. We give a recursive
solution for the one-loop n-gluon QCD amplitudes with three or four
color-adjacent gluons of negative helicity and the remaining ones of positive
helicity. We provide an explicit analytic formula for the QCD amplitude
A_{6;1}(1^-,2^-,3^-,4^+,5^+,6^+), as well as numerical results for
A_{7;1}(1^-,2^-,3^-,4^+,5^+,6^+,7^+), A_{8;1}(1^-,2^-,3^-,4^+,5^+,6^+,7^+,8^+),
and A_{8;1}(1^-,2^-,3^-,4^-,5^+,6^+,7^+,8^+). We expect the on-shell bootstrap
approach to have widespread applications to phenomenological studies at
colliders.Comment: 77 pages, 17 figures; v2, corrected minor typos in text and small
equation
On-Shell Methods in Perturbative QCD
We review on-shell methods for computing multi-parton scattering amplitudes
in perturbative QCD, utilizing their unitarity and factorization properties. We
focus on aspects which are useful for the construction of one-loop amplitudes
needed for phenomenological studies at the Large Hadron Collider.Comment: 49 pages, 15 figures. v2: minor typos correcte
Efficient Color-Dressed Calculation of Virtual Corrections
With the advent of generalized unitarity and parametric integration
techniques, the construction of a generic Next-to-Leading Order Monte Carlo
becomes feasible. Such a generator will entail the treatment of QCD color in
the amplitudes. We extend the concept of color dressing to one-loop amplitudes,
resulting in the formulation of an explicit algorithmic solution for the
calculation of arbitrary scattering processes at Next-to-Leading order. The
resulting algorithm is of exponential complexity, that is the numerical
evaluation time of the virtual corrections grows by a constant multiplicative
factor as the number of external partons is increased. To study the properties
of the method, we calculate the virtual corrections to -gluon scattering.Comment: 48 pages, 23 figure
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