Virtual corrections to $gg\to ZH$ via a transverse momentum expansion

We compute the next-to-leading virtual QCD corrections to the partonic cross section of the production of a Higgs boson in association with a $Z$ boson in gluon fusion. The calculation is based on the recently introduced method of evaluating the amplitude via an expansion in terms of a small transverse momentum. We generalize the method to the case of different masses in the final state and of a process not symmetric in the forward-backward direction exchange. Our analytic approach gives a very good approximation (better than percent) of the partonic cross section in the center of mass energy region up to $\sim 750\text{GeV}$, where at the LHC $\sim 98\mathrm{\%}$ of the total hadronic cross section is concentrated.