The decay $A^0\to h^0 Z^{(*)}$ in the inverted hierarchy scenario and its detection prospects 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 $A^0\to h^0 Z$ (with $m_{h^0}=125$ GeV and $Z$ on-shell). In the absence of any signal, limits on the parameter space of $[\tan\beta, \cos(\beta-\alpha), m_{A^0}]$ in each 2HDM are derived for $m_{A^0} > 225$ GeV. In this work we consider the scenario of inverted hierarchy with $m_{h^0}<125$ GeV and $m_{H^0}=125$ GeV in which the decay $A^0\to h^0 Z^{(*)}$ (i.e. including the case of an off-shell $Z$) can have a large branching ratio in the 2HDM (Type I) for $m_{A^0}<225$ GeV. We calculate the signal cross section $\sigma(gg\to A^0)\times {\rm BR}(A^0\to h^0Z^{(*)})\times {\rm BR}(h^0\to b\overline b)$ in the 2HDM (Type I) with NFC and compare its magnitude with the cross section for the case of normal hierarchy ($m_{h^0}=125$ GeV) that is currently being searched for at the LHC. For the experimentally unexplored region $m_{A^0} < 225$ GeV it is shown that the above cross section for signal events in the scenario of inverted hierarchy can be of the order of a few picobarns. Such sizeable cross sections are several orders of magnitude larger than the cross sections for the case of normal hierarchy, thus motivating an extension of the ongoing searches for $A^0\to h^0 Z^{(*)}$ to probe the scenario of inverted hierarchy.