Neutral Higgs Boson Pair-Production and Trilinear Self-Couplings in the MSSM at ILC and CLIC Energies

We study pair-production as well as the triple self-couplings of the neutral Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) at the Future International Linear $e^{+}e^{-}$ Collider (ILC) and Compact Linear Collider (CLIC). The analysis is based on the reactions $e^{+}e^{-}\to b \bar b h_ih_i, t \bar t h_ih_i$ with $h_i=h, H, A$. We evaluate the total cross-section for both $b\bar bh_ih_i$, $t\bar th_ih_i$ and calculate the total number of events considering the complete set of Feynman diagrams at tree-level. We vary the triple couplings $\kappa\lambda_{hhh}$, $\kappa\lambda_{Hhh}$, $\kappa\lambda_{hAA}$, $\kappa\lambda_{HAA}$, $\kappa\lambda_{hHH}$ and $\kappa\lambda_{HHH}$ within the range $\kappa=-1$ and +2. The numerical computation is done for the energies expected at the ILC with a center-of-mass energy 500, 1000, 1600 $GeV$ and a luminosity 1000 $fb^{-1}$. The channels $e^{+}e^{-}\to b \bar b h_ih_i$ and $e^{+}e^{-}\to t \bar t h_ih_i$ are also discussed to a center-of-mass energy of 3 $TeV$ and luminosities of 1000 $fb^{-1}$ and 5000 $fb^{-1}$.