In this paper, we (Zvi Bern, David Kosower and I) give the complete set of analytical formulae for the one-loop amplitudes (the virtual next-to-leading order QCD corrections) for a vector boson (a photon, W or Z) to make a transition to four partons - either two quarks and two gluons, or four quarks.
The amplitudes are calculated in the helicity formalism, so that all spin information is retained. The results are also crossing symmetric, so they can be used in a variety of next-to-leading order QCD calculations. They were first used in the calculation of the e+e- to four jet rate at next-to-leading-order (NLO) in the strong coupling constant alpha_s, which has been measured experimentally at SLAC and at LEP. The same formulae can also be used in NLO studies of the production of a W or Z plus two jets at the Tevatron or LHC (they were first used in this way in MCFM, and now in BlackHat+SHERPA).
The one-loop four-parton amplitudes also form a part of the calculation of the next-to-next-to-leading order (NNLO) e+e- to three-jet rate, which provides a high precision, high momentum transfer measurement of alpha_s. See e.g. Gehrmann-de Ridder, Gehrmann, Glover and Heinrich, arXiv:0802.0813 [hep-ph].
[ the paper (hep-ph/9708239) ]
[ pdf file of guide to Maple and Mathematica expressions ]
[ file containing Mathematica expressions ]
[ file containing Maple expressions ]
[ sample numerical evaluation of expressions (4q only, at the moment) ]
[ All e+e- to 2q2g helicity amplitudes on one page (use your magnifying glass!!!) ]
e-mail: lance@DUMMY_NAMEslac.stanford.edu; telephone: (650)-926-2627; fax: (650)-926-2525
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