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Light charged Higgs boson with dominant decay to a charm quark and a bottom quark and its search at LEP2 and future $e^+e^-$ colliders

The possibility of a light charged Higgs boson $H^\pm$ that decays predominantly to $cb$ and with a mass in the range 80 GeV $\le M_{H^\pm} \le 90$ GeV is studied in the context of a 3-Higgs Doublet Model (3HDM). Searches for this decay at the Large Hadron Collider (LHC) do not have sensitivity to this mass region at present. It is shown that the searches for $H^\pm$ at LEP2 could be supplemented by either one or two $b$-tags, which would enable such large branching ratios for $H^\pm\to cb$ to be probed in the above mass region. We comment on the possibility of this 3HDM scenario to explain a slight excess in the searches for $H^\pm$ at LEP2, which is best fit by $M_{H^\pm}$ of around 90 GeV, and discuss the prospects for detecting $H^\pm \to cb$ decays at future $e^+e^-$ colliders.