56 research outputs found
Two loop vertices and tree level multicollinear limits in QCD
We present a summary of the methods required to solve loop-integrals and their reduction to Master Integrals. We then present the expansion in d = 4 - 2e of the Master Integrals required for the two loop massless vertex diagrams with three off-shell legs. The results are analytic and contain a new class of two-dimensional harmonic polylogarithms, which match onto the allowed phase-space boundary for the 1→2 process. These Master Integrals are relevant for the QCD corrections to Н → V*V* (where V = W,Z) and for two-loop studies of the triple gluon (and quark-gluon) vertex. We consider multi-parton collinear limits of QCD amplitudes at tree level. Using the MHV formalism we specify the underlying analytic structure of the resulting multi- collinear splitting functions. We adapt the MHV-rules to enable us to derive splitting functions without the need to evaluate the full amplitude. We derive general results for these splitting functions that are valid for specific numbers of negative helicity partons and an arbitrary number of positive helicity partons (or vice versa). Our method can be used to find splitting amplitudes with higher numbers of negative helicity partons. We present new results describing the collinear limits of up to six gluons and up to four partons. These results will have applications in the evaluation of higher order corrections to QCD cross-sections and jet evolution
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
Differential equations and high-energy expansion of two--loop diagrams in D dimensions
New method of calculation of master integrals using differential equations
and asymptotical expansion is presented. This method leads to the results exact
in space-time dimension having the form of the convergent power series. As
an application of this method, we calculate the two--loop master integral for
"crossed--triangle" topology which was previously known only up to O(\ep)
order. The case when a topology contains several master integrals is also
considered. We present an algorithm of the term-by-term calculation of the
asymptotical expansion in this case and analyze in detail the "crossed--box"
topology with three master integrals.Comment: 13 pages,8 figures, uses elsart.cls. Misprints correcte
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
Non-renormalization of the full <VVA> correlator at two-loop order
By explicit calculation of the two-loop QCD corrections we show that for
singlet axial and vector currents the full off-shell correlation function
in the limit of massless fermions is proportional to the one-loop result, when
calculated in the MS-bar scheme. By the same finite renormalization which is
needed to make the one-loop anomaly exact to all orders, we arrive at the
conclusion that two-loop corrections are absent altogether, for the complete
correlator not only its anomalous part. In accordance with the one-loop nature
of the correlator, one possible amplitude, which seems to be missing by
accident at the one-loop level, also does not show up at the two-loop level.Comment: 6 pages, 1 figur
Harmonic polylogarithms for massive Bhabha scattering
One- and two-dimensional harmonic polylogarithms, HPLs and GPLs, appear in
calculations of multi-loop integrals. We discuss them in the context of
analytical solutions for two-loop master integrals in the case of massive
Bhabha scattering in QED. For the GPLs we discuss analytical representations,
conformal transformations, and also their transformations corresponding to
relations between master integrals in the s- and t-channel.Comment: 6 pages, latex, uses espcrc2.sty, contrib. to Proc. of X. Int.
Workshop on Advanced Computing and Analysis Techniques in Physics Research
(ACAT), May 22 - 27, 2005, DESY, Zeuthen, Germany, to appear in NI
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
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