Analysis of the $gg\to H\to hh\to4\tau$ process in the 2HDM lepton specific model at the LHC

We analyse the signature of a light Higgs boson pair in the 2-Higgs Doublet Model(2HDM) Type-X (or lepton specific) over the parameter spaces allowed by theoretical self-consistency requirements as well as the latest experimental constraints from the Large Hadron Collider (LHC), precision test data and $B$ physics. Over the viable regions of the latter, wherein the Standard Model (SM)-like Higgs boson discovered at the LHC in 2012 is the heavier CP-even state of the 2HDM, $H$, it is found that the SM-like Higgs boson can decay into a pair of the lighter CP-even Higgs boson, $h$, via the process $H\to hh$ with a Branching Ratio (BR) of $5\%-10\%$ or so, (with $2 m_h < m_H =125$ GeV). Furthermore, in the Type-X scenario, the lighter Higgs bosons $h$ can dominantly decay into two $\tau$'s due to a large $\tan\beta$. Therefore, the pair of lighter Higgs bosons can altogether decay into a 4 $\tau$ final state. In order to suppress the huge SM background events, we confine ourself to consider the fraction of signal events with two Same-Sign (SS) $\tau$'s further decaying into same sign leptons while the other two $\tau$'s decay hadronically. By using Monte Carlo (MC) and Machine Learning (ML) tools, we thus focus on the analysis of the signal process $pp\to H\to hh\to \tau^{+}\tau^{-}\tau^{+}\tau^{-}\to \ell v_\ell \ell v_\ell \tau_h \tau_h$ (where $\ell= e, \mu$ and $\tau_h$ means a hadronic decay of the $\tau$) and explore the feasibility of such a search at the LHC for a collision energy $\sqrt{s}=~\text{14 TeV}$ and a luminosity $\text{300}~\text{fb}^{-1}$