15 research outputs found
A comparison of efficient methods for the computation of Born gluon amplitudes
We compare four different methods for the numerical computation of the pure
gluonic amplitudes in the Born approximation. We are in particular interested
in the efficiency of the various methods as the number n of the external
particles increases. In addition we investigate the numerical accuracy in
critical phase space regions. The methods considered are based on (i)
Berends-Giele recurrence relations, (ii) scalar diagrams, (iii) MHV vertices
and (iv) BCF recursion relations.Comment: 20 page
Color-dressed recursive relations for multi-parton amplitudes
Remarkable progress inspired by twistors has lead to very simple analytic
expressions and to new recursive relations for multi-parton color-ordered
amplitudes. We show how such relations can be extended to include color and
present the corresponding color-dressed formulation for the Berends-Giele, BCF
and a new kind of CSW recursive relations. A detailed comparison of the
numerical efficiency of the different approaches to the calculation of
multi-parton cross sections is performed.Comment: 31 pages, 4 figures, 6 table
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
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
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
From Trees to Loops and Back
We argue that generic one-loop scattering amplitudes in supersymmetric
Yang-Mills theories can be computed equivalently with MHV diagrams or with
Feynman diagrams. We first present a general proof of the covariance of
one-loop non-MHV amplitudes obtained from MHV diagrams. This proof relies only
on the local character in Minkowski space of MHV vertices and on an application
of the Feynman Tree Theorem. We then show that the discontinuities of one-loop
scattering amplitudes computed with MHV diagrams are precisely the same as
those computed with standard methods. Furthermore, we analyse collinear limits
and soft limits of generic non-MHV amplitudes in supersymmetric Yang-Mills
theories with one-loop MHV diagrams. In particular, we find a simple explicit
derivation of the universal one-loop splitting functions in supersymmetric
Yang-Mills theories to all orders in the dimensional regularisation parameter,
which is in complete agreement with known results. Finally, we present concrete
and illustrative applications of Feynman's Tree Theorem to one-loop MHV
diagrams as well as to one-loop Feynman diagrams.Comment: 52 pages, 17 figures. Some typos in Appendix A correcte
From Yang-Mills Lagrangian to MHV Diagrams
We prove the equivalence of a recently suggested MHV-formalism to the
standard Yang-Mills theory. This is achieved by a formally non-local change of
variables. In this note we present the explicit formulas while the detailed
proofs are postponed to a future publication.Comment: Latex,11 pages, minor changes, reference added, version to appear in
JHE
Recursive Calculation of One-Loop QCD Integral Coefficients
We present a new procedure using on-shell recursion to determine coefficients
of integral functions appearing in one-loop scattering amplitudes of gauge
theories, including QCD. With this procedure, coefficients of integrals,
including bubbles and triangles, can be determined without resorting to
integration. We give criteria for avoiding spurious singularities and boundary
terms that would invalidate the recursion. As an example where the criteria are
satisfied, we obtain all cut-constructible contributions to the one-loop
n-gluon scattering amplitude, A_n^{oneloop}(...--+++...), with split-helicity
from an N=1 chiral multiplet and from a complex scalar. Using the
supersymmetric decomposition, these are ingredients in the construction of QCD
amplitudes with the same helicities. This method requires prior knowledge of
amplitudes with sufficiently large numbers of legs as input. In many cases,
these are already known in compact forms from the unitarity method.Comment: 36 pages; v2 clarification added and typos fixed, v3 typos fixe
Scattering amplitudes with massive fermions using BCFW recursion
We study the QCD scattering amplitudes for \bar{q}q \to gg and \bar{q}q \to
ggg where q is a massive fermion. Using a particular choice of massive fermion
spinor we are able to derive very compact expressions for the partial spin
amplitudes for the 2 \to 2 process. We then investigate the corresponding 2 \to
3 amplitudes using the BCFW recursion technique. For the helicity conserving
partial amplitudes we again derive very compact expressions, but were unable to
treat the helicity-flip amplitudes recursively, except for the case where all
the gluon helicities are the same. We therefore evaluate the remaining partial
amplitudes using standard Feynman diagram techniques.Comment: 21 page
RI'/SMOM scheme amplitudes for quark currents at two loops
We determine the two loop corrections to the Green's function of a quark
current inserted in a quark 2-point function at the symmetric subtraction
point. The amplitudes for the scalar, vector and tensor currents are presented
in both the MSbar and RI'/SMOM renormalization schemes. The RI'/SMOM scheme two
loop renormalization for the scalar and tensor cases agree with previous work.
The vector current renormalization requires special treatment as it must be
consistent with the Slavnov-Taylor identity which we demonstrate. We also
discuss the possibility of an alternative definition of the RI'/SMOM scheme in
the case of the tensor current.Comment: 36 latex pages, 1 figure, 21 tables, anc directory contains txt file
with data in table