Boost to h → Zγ: From LHC to future e+e- colliders

A precise measurement of the Higgs h -> Z gamma decay is very challenging at the LHC, due to the very low branching fraction and the shortage of kinematic handles to suppress the large SM Z gamma background. We show how such a measurement would be significantly improved by considering Higgs production in association with a hard jet. We compare the prospective HL-LHC sensitivity in this channel with other Higgs production modes where h is fairly boosted, e.g. weak boson fusion, and also to the potential h -> Z gamma measurement achievable with a future e(+)e(-) circular collider (fcc-ee). Finally, we discuss new physics implications of a precision measurement of h -> Z gamma.