One-loop amplitudes for W+3 jet production in hadron collisions

We employ the recently developed method of generalized $D$-dimensional unitarity to compute one-loop virtual corrections to all scattering amplitudes relevant for the production of a $W$ boson in association with three jets in hadronic collisions, treating all quarks as massless.Comment: 26 pages, 5 figures, v2 to agree with published versio

Semi-Numerical Evaluation of One-Loop Corrections

We present a semi-numerical algorithm to calculate one-loop virtual corrections to scattering amplitudes. The divergences of the loop amplitudes are regulated using dimensional regularization. We treat in detail the case of amplitudes with up to five external legs and massless internal lines, although the method is more generally applicable. Tensor integrals are reduced to generalized scalar integrals, which in turn are reduced to a set of known basis integrals using recursion relations. The reduction algorithm is modified near exceptional configurations to ensure numerical stability. To test the procedure we apply these techniques to one-loop corrections to the Higgs to four quark process for which analytic results have recently become available.Comment: 33 pages, 10 figures, some typos fixed and references added, to appear in Phys. Rev. D. v3 corrects a typo in eq. A2

Full one-loop amplitudes from tree amplitudes

We establish an efficient polynomial-complexity algorithm for one-loop calculations, based on generalized $D$-dimensional unitarity. It allows automated computations of both cut-constructible {\it and} rational parts of one-loop scattering amplitudes from on-shell tree amplitudes. We illustrate the method by (re)-computing all four-, five- and six-gluon scattering amplitudes in QCD at one-loop.Comment: 27 pages, revte

A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes

Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and implement the method in a numerical procedure. Our technique can be applied to any one-loop scattering amplitude and offers the possibility that one-loop calculations can be performed in an automatic fashion, as tree-level amplitudes are currently done. Instead of individual Feynman diagrams, the ingredients for our one-loop evaluation are tree-level amplitudes, which are often already known. To study the practicality of this method we evaluate the cut-constructible part of the 4, 5 and 6 gluon one-loop amplitudes numerically, using the analytically known 4, 5 and 6 gluon tree-level amplitudes. Comparisons with analytic answers are performed to ascertain the numerical accuracy of the method.Comment: 29 pages with 8 figures; references updated in rsponse to readers' suggestion

Generalized unitarity at work: first NLO QCD results for hadronic W+3jet production

We compute the leading color, next-to-leading order QCD corrections to the dominant partonic channels for the production of a W boson in association with three jets at the Tevatron and the LHC. This is the first application of generalized unitarity for realistic one-loop calculations. The method performs well in this non-trivial test and offers great promise for the future.Comment: 20 pages, 4 figure

On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case

We develop an algorithm of polynomial complexity for evaluating one-loop amplitudes with an arbitrary number of external particles. The algorithm is implemented in the Rocket program. Starting from particle vertices given by Feynman rules, tree amplitudes are constructed using recursive relations. The tree amplitudes are then used to build one-loop amplitudes using an integer dimension on-shell cut method. As a first application we considered only three and four gluon vertices calculating the pure gluonic one-loop amplitudes for arbitrary external helicity or polarization states. We compare our numerical results to analytical results in the literature, analyze the time behavior of the algorithm and the accuracy of the results, and give explicit results for fixed phase space points for up to twenty external gluons.Comment: 22 pages, 9 figures; v2: references added, version accepted for publicatio

Space-time properties of the higher twist amplitudes

A consistent and intuitive description of the twist-4 corrections to the hadron structure functions is presented in a QCD-improved parton model using time-ordered perturbative theory, where the collinear singularities are naturally eliminated. We identify the special propagators with the backward propagators of partons in time order.Comment: 18 Pages, Latex, 8 Ps figures, To appear in Phys. Rev.

Search for Large Rapidity Gap Events in e^+ e^- Annihilation

We investigate the cross-section for the production of a low-mass colour-singlet cluster in $e^+e^-$ annihilation with a large rapidity gap between the colour-singlet cluster and the other jets. It is argued that such events are the cross-channel analogue of large-rapidity-gap events in deep-inelastic scattering, and therefore could in principle be used to investigate the analytic continuation of the BFKL pomeron to the positive-$t$ kinematic regime, where one would expect the trajectory to pass through glueball states. The cross section can be calculated in perturbative QCD, so that the infrared scale arising from non-perturbative effects, which prevents an exponential fall-off with rapidity gap in the case of deep-inelastic scattering, is absent in $e^+ e^-$ annihilation. Correspondingly, the cross section for such events decreases rapidly with increasing rapidity gap.Comment: LATEX file - 21 pages + 15 figure

New results in perturbative QCD

Three topics in perturbative QCD important for Super-collider physics are reviewed. The topics are: (2 2) jet phenomena calculated in O( sT); new techniques for the calculation of tree graphs; and colour coherence in jet phenomena. 31 refs., 6 figs

Analytic Structure of Three-Mass Triangle Coefficients

``Three-mass triangles'' are a class of integral functions appearing in one-loop gauge theory amplitudes. We discuss how the complex analytic properties and singularity structures of these amplitudes can be combined with generalised unitarity techniques to produce compact expressions for three-mass triangle coefficients. We present formulae for the N=1 contributions to the n-point NMHV amplitude.Comment: 22 pages; v3: NMHV n=point expression added. 7 point expression remove