Seeking the CP-odd Higgs via hrightarrow η_(c,b)ell^+ell^-

We show that the decay rates of the Higgs boson to a pseudoscalar quarkonium and a pair of leptons, $h\to P\ell^+\ell^-$ ($P\in\{\eta_c,\eta_b\}$), can be substantially enhanced in a scenario with two Higgs doublets with a softly broken $\mathbb{Z}_2$ symmetry (2HDM) when the CP-odd Higgs A is light, i.e. $m_A\lesssim m_h$. Depending on the type of 2HDM the enhancement of $\mathcal{B}(h\to \eta_{c,b}\tau^+\tau^-)$ with respect to its Standard Model value can be an order of magnitude larger, i.e. $\mathcal{O}(10^{-6}\div10^{-5})$. The decays $h\to P\ell^+\ell^-$ could therefore provide an efficient channel to investigate the presence of a light CP-odd Higgs $A$ and help to disentangle among various 2HDM scenarios.