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.
Highlights
On-shell contributions, such that the remaining background processes are dominated by offshell gauge boson pair production
The derivation of next-to-next-to-leading order (NNLO) QCD corrections to vector boson pair production can build upon calculational techniques [15, 16] that were originally developed for the Drell-Yan process [17, 18] or for Higgs boson production in gluon fusion [15, 16], which have the same QCD structure due to their colour-neutral final state
We present a public implementation for the numerical evaluation of these amplitudes, which in the future will allow the calculation of NNLO QCD corrections to arbitrary electroweak four-fermion production processes
Summary
The calculation of the two-loop helicity amplitudes can be set up in a way that is independent on the nature of the vector bosons considered, by organising the Feynman diagrams contributing to any such process into different classes. Class A collects all those diagrams where both vector bosons are attached on the external fermion line, such that V1 is adjacent to the quark q(p1). Class B collects all those diagrams where both vector bosons are attached on the external fermion line, such that V1 is adjacent to the antiquark q (p2) These diagrams, in the case of a left-handed (right-handed) quark amplitude, are proportional to LVq 1q LVq 2q (RqV1q RqV2q). Class C contains instead all diagrams where both vector bosons are attached to a fermion loop These diagrams are proportional to the charge weighted sum of the quark flavours, which we denote as NV1V2, depending on nature of the final state bosons. Analytical expressions for the Aj, prior to UV renormalisation and IR subtraction, expressed as linear combinations of masters integrals and retaining full dependence on the dimensions d are available on our project page at HepForge
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