Next-to-leading order QCD predictions forW+3-jet distributions at hadron colliders

Abstract

We present next-to-leading order QCD predictions for a variety of distributions in W þ 3-jet production at both the Tevatron and the Large Hadron Collider. We include all subprocesses and incorporate the decay of the W boson into leptons. Our results are in excellent agreement with existing Tevatron data and provide the first quantitatively precise next-to-leading order predictions for the LHC. We include all terms in an expansion in the number of colors, confirming that the specific leading-color approximation used in our previous study is accurate to within 3%. The dependence of the cross section on renormalization and factorization scales is reduced significantly with respect to a leading-order calculation. We study different dynamical scale choices, and find that the total transverse energy is significantly better than choices used in previous phenomenological studies. We compute the one-loop matrix elements using on-shell methods, as numerically implemented in the BLACKHAT code. The remaining parts of the calculation, including generation of the real-emission contributions and integration over phase space, are handled by the SHERPA package.

One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts

“…Such organization of the calculation ensures that not too much time is spent on the calculation of pieces of the amplitude that give small contributions to the final answer. These ideas have been used in recent NLO calculation of some complicated processes [7,17].…”

“…(5.33) becomesc 35) where the coefficients c k read , we take vectors l that have non-vanishing projections on either n 3 and n ǫ or on n 4 and n ǫ . Since we already know all the cut-constructible coefficients, it is straightforward to findc 7,8,9 . We note that the discrete Fourier transform is just one of many ways to solve the linear system of equations required to obtain the coefficientsc 0 , ...c 6 .…”

“…andc (7) 012 is the relevant, non-evanescent reduction coefficient. To project ontõ c (7) 012 , we begin by performing Laurent expansion at t = ∞, as we did for the cut-constructible part.…”

“…The coefficientc (7) 012 is then obtained by the application of an additional Laurent expansion operator, designed to pick up the O(µ 2 ) term, to the triple cut…”

“…In the past three years, a large number of one-loop computations with four (massive and massless) particles in the final state were completed [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] and even the first 2 → 5 resultsthe NLO QCD corrections to pp → W (Z) + 4j [17,18] -was obtained. 1 Some of this progress is to be attributed to spectacular improvements of the existing Feynman-diagrammatic algorithms for one-loop calculations, whose efficiency and stability was boosted beyond expectations.…”