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We show that the decay rates of the Higgs boson to a pseudoscalar quarkoniumand a pair of leptons, $h\to P\ell^+\ell^-$ ($P\in\{\eta_c,\eta_b\}$), can besubstantially enhanced in a scenario with two Higgs doublets with a softlybroken $\mathbb{Z}_2$ 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 Modelvalue can be an order of magnitude larger, i.e.$\mathcal{O}(10^{-6}\div10^{-5})$. The decays $h\to P\ell^+\ell^-$ couldtherefore provide an efficient channel to investigate the presence of a lightCP-odd Higgs $A$ and help to disentangle among various 2HDM scenarios.

Seeking the CP-odd Higgs via $h\rightarrow \eta_{c,b}\ell^+\ell^-$