D. Forde

An Automated Implementation of On-Shell Methods for One-Loop Amplitudes

We present the first results from BlackHat, an automated C++ program for calculating one-loop amplitudes. The program implements the unitarity method and on-shell recursion to construct amplitudes. As input to the calculation, it uses compact analytic formulae for tree amplitudes for four-dimensional helicity states. The program performs all related computations numerically. We make use of recently developed on-shell methods for evaluating coefficients of loop integrals, introducing a discrete Fourier projection as a means of improving efficiency and numerical stability. We illustrate the numerical stability of our approach by computing and analyzing six-, seven-, and eight-gluon amplitudes in QCD and comparing against previously obtained analytic results.

Direct Extraction of One-loop Integral Coefficients

We present a general procedure for obtaining the coefficients of the scalar bubble and triangle integral functions of one-loop amplitudes. Coefficients are extracted by considering two-particle and triple unitarity cuts of the corresponding bubble and triangle integral functions. After choosing a specific parameterization of the cut loop momentum we can uniquely identify the coefficients of the desired integral functions simply by examining the behavior of the cut integrand as the unconstrained parameters of the cut loop momentum approach infinity. In this way we can produce compact forms for scalar integral coefficients. Applications of this method are presented for both QCD and electroweak processes, including an alternative form for the recently computed three-mass triangle coefficient in the six-photon amplitude A{sub 6}(1{sup -}, 2{sup +}, 3{sup -}, 4{sup +}, 5{sup -}, 6{sup +}). The direct nature of this extraction procedure allows for a very straightforward automation of the procedure.

One-Loop Calculations with BlackHat

We describe BlackHat, an automated C++ program for calculating one-loop amplitudes, and the techniques used in its construction. These include the unitarity method and on-shell recursion. The other ingredients are compact analytic formulae for tree amplitudes for four-dimensional helicity states. The program computes amplitudes numerically, using analytic formula only for the tree amplitudes, the starting point for the recursion, and the loop integrals. We make use of recently developed on-shell methods for evaluating coefficients of loop integrals, in particular a discrete Fourier projection as a means of improving numerical stability. We illustrate the good numerical stability of this approach by computing six-, seven- and eight-gluon amplitudes in QCD and comparing against known analytic results.

Next-to-Leading Order Jet Physics with BlackHat

We present several results obtained using the B LACKHAT next-to-leading order QCD program library, in conjunction with SHERPA. In particular, we present distributions for vector boson plus 1,2,3-jet production at the Tevatron and at the asymptotic running energy of the Large Hadron Collider, including new Z + 3-jet distributions. The Z + 2-jet predictions for the second-jet PT distribution are compared to CDF data. We present the jet-emission probability at NLO in W + 2jet events at the LHC, where the tagging jets are taken to be the ones furthest apart in pseudorapidity. We analyze further the large left-handed W ± polarization, identified in our previous study, for W bosons produced at high PT at the LHC.

NLO Jet Physics with BlackHat

We present several results obtained using the BLACKHAT next-to-leading order QCD program library, in conjunction with SHERPA. In particular, we present distributions for vector boson plus 1,2,3-jet production at the Tevatron and at the asymptotic running energy of the Large Hadron Collider, including new Z + 3-jet distributions. The Z + 2-jet predictions for the second-jet P{sub T} distribution are compared to CDF data. We present the jet-emission probability at NLO in W + 2-jet events at the LHC, where the tagging jets are taken to be the ones furthest apart in pseudorapidity. We analyze further the large left-handed W{sup {+-}} polarization, identified in our previous study, for W bosons produced at high P{sub T} at the LHC.