One-Loop Multi-Parton Amplitudes with a Vector Boson for the LHC

Abstract

In this talk, we present the first, numerically stable, results for the one-loop amplitudes needed for computing W,Z + 3 jet cross sections at the LHC to next-to-leading order in the QCD coupling. We implemented these processes in BlackHat, an automated program based on on-shell methods. These methods scale very well with increasing numbers of external partons, and are applicable to a wide variety of problems of phenomenological interest at the LHC.

Figures (2)

• Figure 1: Sample leading-color diagrams for the amplitudes (a) $q g g {\bar{q}} \, {\bar{l}} l$ and (b) $q g g g{\bar{q}} \, {\bar{l}} l$. The leptons, ${\bar{l}},l$ couple to the quarks via a vector boson, $V$. Analytic expressions for the six-point amplitudes (a) are given in ref. Zqqgg.
• Figure 3: The distribution of the logarithm of the relative error over 100,000 phase-space points, for four independent helicity choices for the $q g g g {\bar{q}} \, {\bar{l}} l$ leading color amplitudes. The helicity labels on the plots indicate the helicities of the three gluons. The dashed (black) curve in each histogram gives the relative error for the $1/\epsilon^2$ part, the solid (red) curve gives the $1/\epsilon$ singularity, and the shaded (blue) distribution gives the finite $\epsilon^0$ component of the corresponding helicity amplitude.