The two-loop helicity amplitudes for $q{\bar{q}}^{\prime }\to V_1{V}_2\to 4\mathrm{leptons}$

Abstract

We compute the two-loop massless QCD corrections to the helicity amplitudes for the production of two massive vector bosons in quark-antiquark annihilation, allowing for an arbitrary virtuality of the vector bosons: $q{\bar{q}}^{\prime }\to V_1{V}_2$. Combining with the leptonic decay currents, we obtain the full two-loop QCD description of the corresponding electroweak four-lepton production processes. The calculation is performed by projecting the two-loop diagrams onto an appropriate basis of Lorentz structures. All two-loop Feynman integrals are reduced to a basis of master integrals, which are then computed using the differential equations method and optimised for numerical performance. We provide a public C++ code which allows for fast and precise numerical evaluations of the amplitudes.

34 pages, 3 figures, results available in computer readable format on HepForge at http://vvamp.hepforge.org ; fixed typos in electroweak coupling definitions, version accepted for publication in JHEP

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