The two-loop helicity amplitudes for $q \bar q' \to V_1 V_2 \to 4~\mathrm{leptons}$

TL;DR

This paper presents the calculation of two-loop QCD corrections to helicity amplitudes for quark-antiquark annihilation into two vector bosons, including their decay into four leptons, enhancing precision in electroweak process predictions.

Contribution

It provides the first complete two-loop QCD calculation for $q ar q' o V_1V_2$ with arbitrary vector boson virtualities, including a public code for numerical evaluation.

Findings

Computed two-loop massless QCD corrections for vector boson production.

Reduced all integrals to master integrals using differential equations.

Provided a public C++ code for fast amplitude evaluations.

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: $q \bar q' \to V_1V_2$. 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.