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