Searching for a Light Higgs Boson via the Yukawa Process at Lepton Colliders

We explore the prospect of Yukawa production of a light boson which can exist in an extended Higgs sector. A particularly interesting case is the light pseudoscalar in Type-X two Higgs doublet model which can explain the anomalous magnetic moment of muon at large $\tan \beta$. Considering ILC $Higgs$ $factory$ with $\sqrt{s}=250$ GeV, we show that the available parameter space can be fully examined by the (tau) Yukawa process at $5\sigma$. We also demonstrate the mass reconstruction of such a light particle which helps to sizably minimize the background events.