Charged Higgs Pair Production in a General Two Higgs Doublet Model at $e^+e^-$ and $\mu^+\mu^-$ Linear Colliders

In this paper, charged Higgs pair production through $\ell^+ \ell^- \rightarrow H^+ H^-$ where $\ell = e$ or $\mu$, is studied within the framework of a general Two Higgs Doublet Model (2HDM). The analysis is relevant to a future $e^+e^-$ or $\mu^+\mu^-$ collider operating at center of mass energy of $\sqrt{s}=500$ GeV. Two different scenarios of small and large $\alpha$ values is studied. Here $\alpha$ is the parameter which diagonalizes the neutral CP-even Higgs boson mass matrix. Within the Minimal Supersymmetric Standard Model (MSSM), cross section of this process is almost the same at $e^+e^-$ and $\mu^+\mu^-$ colliders. It is shown that at $e^+e^-$ colliders within a general 2HDM, cross section is not sensitive to the mass of neutral Higgs bosons, however, it can acquire large values up to several picobarn at $\mu^+\mu^-$ colliders with the presence of heavy neutral Higgs bosons. A scan over Higgs boson mass parameter space is performed to analyze the effect of large masses of neutral Higgs bosons involved in the s-channel propagator and thus in the total cross section of this process.