Probing the decay $A^0\to h^0 Z^{(*)}$ in Two-Higgs-Doublet Models in the inverted hierarchy scenario at the Large Hadron Collider

Searches are being carried out at the Large Hadron Collider (LHC) for the decay of the CP-odd scalar ($A^0$) in Two-Higgs-Doublet Models (2HDMs) with Natural Flavour Conservation (NFC) in the channel $A^0\to h^0 Z$, where $h^0$ is either the discovered 125 GeV Higgs boson or is an undiscovered CP-even scalar with a mass below 125 GeV. The latter possibility is called the "inverted hierarchy scenario" (IH) and would provide the opportunity of simultaneous discovery of two scalars. In both searches the selection cuts are optimised for the case of an on-shell $Z$ boson. For the case of the $Z$ boson being off-shell (denoted by $Z^*$, for which $m_{A^0} - m_{h^0}<m_Z$) no limits are set on the relevant 2HDM parameters from this process. It is known that the decay $A^0\to h^0 Z^*$ can have a large branching ratio (BR) in 2HDMs (especially in the Type I structure). In the context of the IH scenario and developing our previous work, we calculate the signal cross section $\sigma(gg\to A^0)\times {\rm BR}(A^0\to h^0Z^{(*)})\times {\rm BR}(h^0\to b\overline b,\tau\overline \tau)$ in the four types of 2HDMs with NFC. We also suggest some selection cuts that could provide sensitivity to $A^0\to h^0 Z^*$ in the IH scenario.