We summarise the calculation of the two-loop next-to-leading order QCD corrections to Z boson plus Higgs boson production in gluon fusion.
The result presented includes full top-quark mass effects and is obtained by combining two-loop virtual contributions computed numerically, using sector decomposition, with virtual contributions obtained in a high-energy expansion.
We find that the corrections enhance the cross-section by approximately a factor of 2 and reduce the renormalisation and factorisation scale uncertainty by around $30\%$.
For a centre of mass energy of $\sqrt{s}=13.6\ \mathrm{TeV}$ we obtain
\begin{equation*}
\sigma_{gg\rightarrow ZH}^{\mathrm{NLO}(m_t^\mathrm{OS})} = 114.7(3)^{+16.2\%}_{-13.7\%}\ \mathrm{fb}.
\end{equation*}
We also observe that the choice of top-quark mass renormalisation scheme can have a significant impact on the prediction.