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

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.

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

CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes

We present a program that implements the OPP reduction method to extract the coefficients of the one-loop scalar integrals from a user defined (sub)-amplitude or Feynman Diagram, as well as the rational terms coming from the 4-dimensional part of the numerator. The rational pieces coming from the epsilon-dimensional part of the numerator are treated as an external input, and can be computed with the help of dedicated tree-level like Feynman rules. Possible numerical instabilities are dealt with the help of arbitrary precision routines, that activate only when needed.Comment: Version published in JHE

Dijet Production at Large Rapidity Intervals

We examine dijet production at large rapidity intervals at Tevatron energies, by using the theory of Lipatov and collaborators which resums the leading powers of the rapidity interval. We analyze the growth of the Mueller-Navelet $K$-factor in this context and find it to be negligible. However, we do find a considerable enhancement of jet production at large transverse momenta. In addition, we show that the correlation in transverse momentum and azimuthal angle of the tagging jets fades away as the rapidity interval is increased.Comment: 12 pages, preprint DESY 93-139, SCIPP 93/3

Choosing integration points for QCD calculations by numerical integration

I discuss how to sample the space of parton momenta in order to best perform the numerical integrations that lead to a calculation of three jet cross sections and similar observables in electron-positron annihilation.Comment: 25 pages with 8 figure

Spin-dependent structure functions g^1\hat g_1 and g^2\hat g_2 for inclusive spin-half baryon production in electron-positron annihilation

Two spin-dependent structure functions $\hat g_1$ and $\hat g_2$ for the inclusive spin-half baryon production in electron-positron annihilation are studied in the context of QCD factorization as well as in the naive quark parton model. As a result, it is found that the sum of $\hat g_1$ and $\hat g_2$ is related to $\hat h_1$ and $\hat g_T$, two quark fragmentation functions defined by Jaffe and Ji. In connection with the measurement of quark fragmentation functions, the possible phenomenological consequences are discussed.Comment: RevTex, four 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

On azimuthal spin correlations in Higgs plus jet events at LHC

We consider the recent proposal that the distribution of the difference between azimuthal angles of the two accompanying jets in gluon-fusion induced Higgs-plus-two-jet events at LHC reflects the CP of the Higgs boson produced. We point out that the hierarchy between the Higgs boson mass and the jet transverse energy makes this observable vulnerable to logarithmically enhanced higher-order perturbative corrections. We present an evolution equation that describes the scale variation of the azimuthal angular correlation for the two jets. The emission of extra partons leads to a significant suppression of the correlation. Using the HERWIG Monte Carlo event generator, we carry out a parton-shower analysis to confirm the findings.Comment: Published version. 11 pages, 4 figures, uses JHEP3.cl