Prospects for Detecting light bosons at the FCC-ee and CEPC

We look at the prospects for detecting light bosons, $X$, at proposed Z factories assuming a production of ${10}^{12}$ Z bosons. Such a large yield is within the design goals of future FCC-ee and CEPC colliders. Specifically we look at the cases where $X$ is either a singlet scalar which mixes with the standard model Higgs or a vector boson with mass $1\lesssim M_X\lesssim 80$ GeV. We find that several channels are particularly promising for discovery prospects. In particular $Z\to f\bar{f}X$ and $Z\to V_{Q}X$ gives a promising signal above a very clean standard model background. We also discuss several channels that have too large a background to be useful.