Abstract
We study the production of two electroweak vector bosons in association with a jet via gluon fusion. In particular we consider the production of $\ensuremath{\gamma}Zg$, $ZZg$ and ${W}^{+}{W}^{\ensuremath{-}}g$ at hadron colliders and compute their cross sections. Such processes have already produced a large number of events at the Large Hadron Collider by now. These processes can be background to the Higgs boson production and a number of beyond the standard model scenarios. Therefore it is important to know the values of their contribution. The calculation is based on conventional Feynman diagram approach. In particular we find that the process $gg\ensuremath{\rightarrow}ZZg$ can make a significant contribution to the process $pp\ensuremath{\rightarrow}ZZ+\mathrm{\text{jet}}$.
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