Sources of Charged Higgs Pair Through Double or Triple Higgs Production in Two Higgs Doublet Model Type II at Linear Colliders

The production of triple Higgs $(H^+H^-H^0)$, $(H^+H^-h^0)$ and pair wise charged Higgs boson $(H^+H^-)$ is studied in the context of future linear colliders within the Two-Higgs Doublet Model (2HDM) type II. The aim is to compare sources of charged Higgs pair through the above processes, i.e., double and triple Higgs production. Cross-sections are calculated at the leading order in 2HDM type II and Minimal Supersymmetric Standard Model (MSSM). Several orders of magnitude ($\sim 10^{4}$) enhancement is observed in 2HDM compared to MSSM, while no sizable enhancement is seen in muon collider versus electron-positron collider. The analysis is based on a heavy charged Higgs with mass above 500 GeV. It is found that double charged Higgs production cross-section (being the same in 2HDM and MSSM) is few femtobarns while the triple Higgs production can not exceed a fraction of femtobarn within the parameter space under study.