# The two-loop helicity amplitudes for $q\overline{q}^{\prime}\to {V}_1{V}_2\to 4$ - Zurich Open Repository and Archive

Gehrmann, Thomas; von Manteuffel, Andreas; Tancredi, Lorenzo (2015). The two-loop helicity amplitudes for $q\overline{q}^{\prime}\to {V}_1{V}_2\to 4$. Journal of High Energy Physics, 2015(9):128.

## 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.

## 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.

## Citations

10 citations in Web of Science®
4 citations in Scopus®

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Physics Institute 530 Physics English September 2015 15 Feb 2016 15:29 05 Apr 2016 20:02 Springer 1029-8479 Publisher DOI. An embargo period may apply. https://doi.org/10.1007/JHEP09(2015)128 http://arxiv.org/abs/1503.04812 (Organisation)

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