Associated 𝑍 𝐻 production plays a special role in the determination of Higgs properties at the
LHC. An improved theoretical control over the 𝑔𝑔 → 𝑍 𝐻 subprocess is important to reduce the
scale uncertainties in the SM prediction. We present the calculation of the virtual QCD corrections
to 𝑔𝑔 → 𝑍 𝐻 using an analytic approximation, based on the expansion of the amplitude in terms
of a small transverse momentum of the final particles. We also report on the combination of
these results with those obtained from a complementary approach, based on the expansion of the
amplitude in the high-energy limit. When the results of both expansions are improved using Padé
approximants, their combination provides an accurate approximation over the whole phase space.