The two-loop helicity amplitudes for gg → V 1 V 2 → 4 leptons

Andreas Von Manteuffel,Lorenzo Tancredi

doi:10.1007/jhep06(2015)197

Abstract

We compute the two-loop massless QCD corrections to the helicity amplitudes for the production of two electroweak gauge bosons in the gluon fusion channel, gg → V 1 V 2, keeping the virtuality of the vector bosons V 1 and V 2 arbitrary and taking their decays into leptons into account. The amplitudes are expressed in terms of master integrals, whose representation has been optimised for fast and reliable numerical evaluation. We provide analytical results and a public C++ code for their numerical evaluation on HepForge at http://vvamp.hepforge.org .

Highlights

JHEP06(2015)197 can be important in order to achieve a description of the full process which matches the experimental precision
We provide analytical results and a public C++ code for their numerical evaluation on HepForge at http://vvamp.hepforge.org
The calculation builds upon the master integrals for four-point functions with massless propagators and two massive external legs, which were computed recently in the case of equal masses in [34, 35], and in the case of different masses in [36,37,38,39]. The former were used for the first NNLO fully-inclusive calculations of ZZ [3] and W +W − [4] production at the LHC, while the latter allowed the computation of the two-loop corrections to qq → V1V2 [39, 40]

Summary

Calculation of the form factors

The calculation of the coefficients Ejλ1λ2 proceeds as follows. We produce all one- and two-loop Feynman diagrams relevant for gg → V1V2 using Qgraf [46]. The described version of our code implements a minimal set of 9 coefficients Aj and employs four evaluations of them with different kinematics in order to derive the remaining form factors using crossing relations. If required, it is straight-forward to further improve the evaluation speed, either by proper caching of multiple polylogarithms or, at the price of an increased code size, by an explicit implementation of all form factors, as we did for the process qq → V1V2 in [39]. For the physical helicity amplitudes (3.12) we wish to point out that an additional dampening (very) close to the aforementioned phase space boundaries should be taken into account due to the additional overall factors CLL and CLR (3.13)

Conclusions

A Form factor relations