Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity

We compute a complete set of independent leading-color two-loop five-parton amplitudes in QCD. These constitute a fundamental ingredient for the next-to-next-to-leading order QCD corrections to three-jet production at hadron colliders. We show how to consistently consider helicity amplitudes with external fermions in dimensional regularization, allowing the application of a numerical variant of the unitarity approach. Amplitudes are computed by exploiting a decomposition of the integrand into master and surface terms that is independent of the parton type. Master integral coefficients are numerically computed in either finite-field or floating-point arithmetic and combined with known analytic master integrals. We recompute two-loop leading-color four-parton amplitudes as a check of our implementation. Results are presented for all independent four- and five-parton processes including contributions with massless closed fermion loops.Comment: v3: corrected wrong signs for five-gluon $N_f^2$ amplitudes with vanishing tree

W- and Z-boson production with a massive bottom-quark pair at the Large Hadron Collider

We present total and differential cross sections for W b anti-b and Z b anti-b production at the CERN Large Hadron Collider with a center-of-mass energy of 14 TeV, including Next-to-Leading Order (NLO) QCD corrections and full bottom-quark mass effects. We also provide numerical results obtained with a center-of-mass energy of 10 TeV. We study the scale uncertainty of the total cross sections due to the residual renormalization- and factorization-scale dependence of the truncated perturbative series. While in the case of Z b anti-b production the scale uncertainty of the total cross section is reduced by NLO QCD corrections, the W b anti-b production process at NLO in QCD still suffers from large scale uncertainties, in particular in the inclusive case. We also perform a detailed comparison with a calculation that considers massless bottom quarks, as implemented in the Monte Carlo program MCFM. The effects of a non-zero bottom-quark mass (m_b) cannot be neglected in phase-space regions where the relevant kinematic observable, such as the transverse momentum of the bottom quarks or the invariant mass of the bottom-quark pair, are of the order of m_b. The effects on the total production cross sections are usually smaller than the residual scale uncertainty at NLO in QCD.Comment: 24 pages, 24 postscript figures, added one reference, a few typos corrected, version published in PR

Associated Production of a W Boson and One b Jet

We calculate the production of a W boson and a single b jet to next-to-leading order in QCD at the Fermilab Tevatron and the CERN Large Hadron Collider. Both exclusive and inclusive cross sections are presented. We separately consider the cross section for jets containing a single b quark and jets containing a b-anti b pair. There are a wide variety of processes that contribute, and it is necessary to include them all in order to have a complete description at both colliders.Comment: LaTeX, 16 pages, 22 postscript figures; version published in Phys. Rev.

Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders

We present the complete set of leading-color two-loop contributions required to obtain next-to-next-to-leading-order (NNLO) QCD corrections to three-jet production at hadron colliders. We obtain analytic expressions for a generating set of finite remainders, valid in the physical region for three-jet production. The analytic continuation of the known Euclidean-region results is determined from a small set of numerical evaluations of the amplitudes. We obtain analytic expressions that are suitable for phenomenological applications and we present a C++ library for their efficient and stable numerical evaluation.Comment: Analytic results in ancillary files; link for numerical code in references. v3: matches the published versio