Diboson production in the SMEFT from gluon fusion

Precision measurements of diboson production at the LHC is an important probe of the limits of the Standard Model. The gluon-fusion channel of this process offers a connection between the Higgs and top sectors. We study in a systematic way gluon-induced diboson production in the Standard Model Effective Field Theory. We compute the amplitudes of double Higgs, double $Z\mathrm{/}W$ and associated $ZH$ production at one loop and with up to one insertion of a dimension-6 operator. We study their high-energy limit and identify to which operators each channel could be most sensitive. To illustrate the relevance of these processes, we perform a phenomenological study of associated $ZH$ production. We show that for some top operators the gluon-induced channel can offer competitive sensitivity to constraints obtained from top quark production processes.