Leading-Color Two-Loop Amplitudes for Four Partons and a W Boson in QCD

Abstract

We present the leading-color two-loop QCD corrections for the scattering of four partons and a $W$ boson, including its leptonic decay. The amplitudes are assembled from the planar two-loop helicity amplitudes for four partons and a vector boson decaying to a lepton pair, which are also used to determine the planar two-loop amplitudes for four partons and a $Z/{\gamma }^{\ast }$ boson with a leptonic decay. The analytic expressions are obtained by setting up a dedicated Ansatz and constraining the free parameters from numerical samples obtained within the framework of numerical unitarity. The large linear systems that must be solved to determine the analytic expressions are constructed to be in Vandermonde form. Such systems can be very efficiently solved, bypassing the bottleneck of Gaussian elimination. Our results are expressed in a basis of one-mass pentagon functions, which opens the possibility of their efficient numerical evaluation.

31 pages, 5 figures; v3: matches the published version; analytic expressions at http://www.hep.fsu.edu/~ffebres/W4partons

References in corpus (20)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Algorithm FIRE -- Feynman Integral REduction
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• FIRE5: a C++ implementation of Feynman Integral REduction
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders
• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Measurements of the W production cross sections in association with jets with the ATLAS detector
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• Cluster algebras for Feynman integrals
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Multi-Quark Colour Decompositions from Unitarity
• Measurement of the differential cross sections for the associated production of a W boson and jets in proton-proton collisions at sqrt(s) = 13 TeV
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations

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