Gluon Fusion Contribution to $VHj$ Production at Hadron Colliders

We study the associated production of an electroweak vector boson and the Higgs boson with a jet via gluon-gluon fusion. At the leading order, these processes occur at one-loop level. The amplitudes of these one-loop processes are gauge invariant and finite. Therefore, their contributions towards the corresponding hadronic cross sections and kinematic distributions can be calculated separately. We present results for the Large Hadron Collider and its discussed upgrades. We find that the gluon-gluon one-loop process gives dominant contribution to the $\gamma H j$ production. We observe a destructive interference effect in the $gg\to Z H j$ amplitude. We also find that in the high transverse momentum and central rapidity region, the $ZHj$ production cross section via gluon-gluon fusion becomes comparable to the cross section contributions coming from quark-quark and quark-gluon channels.