Reconstructing heavy Higgs boson masses in a type X two-Higgs-doublet model with a light pseudoscalar particle

We analyze the prospects of reconstructing the mass of a heavy charged Higgs boson 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 favored if one wants to explain the muon anomalous magnetic moment. The associated production of charged Higgs bosons with the pseudoscalar A and subsequent decay of the charged Higgs boson into a W and A is found to be our relevant channel. The branching ratio for H⁺→W⁺A with M_H⁺~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 bosons. The neutral heavy Higgs boson, being degenerate with the charged Higgs boson for most of the allowed parameter space of the model, also contributes to similar final states. Thus, both the charged and neutral $CP$-even heavy Higgs bosons are reconstructed within a band of about 10 GeV.