The Triple Higgs Boson Self-Coupling at Future Linear e+e- Colliders Energies: ILC and CLIC

We analyzed the triple Higgs boson self-coupling at future $e^{+}e^{-}$ colliders energies, with the reactions $e^{+}e^{-}\to b \bar b HH, t \bar t HH$. We evaluate the total cross-sections for both $b\bar bHH$ and $t\bar tHH$, and calculate the total number of events considering the complete set of Feynman diagrams at tree-level. We vary the triple coupling $\kappa\lambda_{3H}$ within the range $\kappa=-1$ and +2. The numerical computation is done for the energies expected to be available at a possible Future Linear $e^{+}e^{-}$ Collider with a center-of-mass energy $800, 1000, 1500$ $GeV$ and a luminosity 1000 $fb^{-1}$. Our analysis is also extended to a center-of-mass energy 3 $TeV$ and luminosities of 1000 $fb^{-1}$ and 5000 $fb^{-1}$. We found that for the process $e^{+}e^{-}\to b \bar b HH$, the complete calculation differs only by 3% from the approximate calculation $e^{+}e^{-}\to ZHH(Z\to b\bar b)$, while for the process $e^{+}e^{-}\to t \bar tHH$, the expected number of events, considering the decay products of both $t$ and $H$, is not enough to obtain an accurate determination of the triple Higgs boson self-coupling.