Reconstructing heavy Higgs boson masses in Type X Two-Higgs Doublet Model with a light pseudoscalar

We analyze the prospects of reconstructing the mass of a heavy charged Higgs boson %have been analyzed in the context of a Type X two-Higgs doublet model where a light pseudoscalar $A$ in the mass range $40-60$ GeV is phenomenologically allowed, and is in fact favoured if one wants to explain the muon anomalous magnetic moment. The associated production of charged Higgs with the pseudoscalar $A$ and subsequent decay of the charged Higgs into a $W$ and $A$, is found to be our relevant channel. The branching ratio for $H^+ \to W^+ A$ with $M_{H^+} \sim 200$ GeV, is close to 50\%. The hadronic decay of the $W$ boson, coupled with the leptonic decays of $A$ into a tau and muon pair, help in identifying the charged Higgs. The neutral heavy Higgs, being degenerate with the charged Higgs for most of the allowed parameter space of the model, also contributes to similar final states. Thus both of these particles are reconstructed within a band of about 10 GeV.