143 research outputs found
QCD recursion relations from the largest time equation
We show how by reassembling the tree level gluon Feynman diagrams in a
convenient gauge, space-cone, we can explicitly derive the BCFW recursion
relations. Moreover, the proof of the gluon recursion relations hinges on an
identity in momentum space which we show to be nothing but the Fourier
transform of the largest time equation. Our approach lends itself to natural
generalizations to include massive scalars and even fermions.Comment: 18 pages, 2 figures, minor changes to Sect.
Multigluon tree amplitudes with a pair of massive fermions
We consider the calculation of n-point multigluon tree amplitudes with a pair
of massive fermions in QCD. We give the explicit transformation rules of this
kind of massive fermion-pair amplitudes with respect to different reference
momenta and check the correctness of them by SUSY Ward identities. Using these
rules and onshell BCFW recursion relation, we calculate the analytic results of
several n-point multigluon amplitudes.Comment: 15page
On Tree Amplitudes in Gauge Theory and Gravity
The BCFW recursion relations provide a powerful way to compute tree
amplitudes in gauge theories and gravity, but only hold if some amplitudes
vanish when two of the momenta are taken to infinity in a particular complex
direction. This is a very surprising property, since individual Feynman
diagrams all diverge at infinite momentum. In this paper we give a simple
physical understanding of amplitudes in this limit, which corresponds to a hard
particle with (complex) light-like momentum moving in a soft background, and
can be conveniently studied using the background field method exploiting
background light-cone gauge. An important role is played by enhanced spin
symmetries at infinite momentum--a single copy of a "Lorentz" group for gauge
theory and two copies for gravity--which together with Ward identities give a
systematic expansion for amplitudes at large momentum. We use this to study
tree amplitudes in a wide variety of theories, and in particular demonstrate
that certain pure gauge and gravity amplitudes do vanish at infinity. Thus the
BCFW recursion relations can be used to compute completely general gluon and
graviton tree amplitudes in any number of dimensions. We briefly comment on the
implications of these results for computing massive 4D amplitudes by KK
reduction, as well understanding the unexpected cancelations that have recently
been found in loop-level gravity amplitudes.Comment: 22 pages, 3 figure
On-shell recursion relations for all Born QCD amplitudes
We consider on-shell recursion relations for all Born QCD amplitudes. This
includes amplitudes with several pairs of quarks and massive quarks. We give a
detailed description on how to shift the external particles in spinor space and
clarify the allowed helicities of the shifted legs. We proof that the
corresponding meromorphic functions vanish at z --> infinity. As an application
we obtain compact expressions for helicity amplitudes including a pair of
massive quarks, one negative helicity gluon and an arbitrary number of positive
helicity gluons.Comment: 30 pages, minor change
SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks
We use supersymmetric Ward identities to relate multi-gluon helicity
amplitudes involving a pair of massive quarks to amplitudes with massive
scalars. This allows to use the recent results for scalar amplitudes with an
arbitrary number of gluons obtained by on-shell recursion relations to obtain
scattering amplitudes involving top quarks.Comment: 22 pages, references adde
MHV Techniques for QED Processes
Significant progress has been made in the past year in developing new `MHV'
techniques for calculating multiparticle scattering amplitudes in Yang-Mills
gauge theories. Most of the work so far has focussed on applications to Quantum
Chromodynamics, both at tree and one-loop level. We show how such techniques
can also be applied to abelian theories such as QED, by studying the simplest
tree-level multiparticle process, e^+e^- to n \gamma. We compare explicit
results for up to n=5 photons using both the Cachazo, Svrcek and Witten `MHV
rules' and the related Britto-Cachazo-Feng `recursion relation' approaches with
those using traditional spinor techniques.Comment: 19 pages, 10 figures. References adde
Recursion relations, Helicity Amplitudes and Dimensional Regularization
Using the method of on-shell recursion relations we compute tree level
amplitudes including D-dimensional scalars and fermions. These tree level
amplitudes are needed for calculations of one-loop amplitudes in QCD involving
external quarks and gluons.Comment: 28 pages, 6 figures, clarifications adde
A direct proof of the CSW rules
Using recursion methods similar to those of Britto, Cachazo, Feng and Witten
(BCFW) a direct proof of the CSW rules for computing tree-level gluon
amplitudes is given.Comment: 11 pages, uses axodraw.st
One-loop helicity amplitudes for H -> gluons: the all-minus configuration
We use twistor inspired rules to compute the one-loop amplitude for a Higgs
boson coupling to any number of negative helicity gluons in the large top mass
limit.Comment: 5 pages, talk given at the conference "Loops and Legs in Quantum
Field Theory", Eisenach, Germany, April 2006. Corrected typo
Seven parton amplitudes from recursion relations
We present the first calculation of two-quark and five-gluon tree amplitudes
using on-shell recursion relations. These amplitudes are needed for tree level
5-jet cross-section and an essential ingredient for next-to-leading order 4-jet
and next-to-next-to-leading order 3-jet production at hadronic colliders. Very
compact expressions for all possible helicity configurations are provided,
allowing for direct implementation in Monte-Carlo codes.Comment: 11 page
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