Analysis of trilinear Higgs self coupling in Two Higgs Doublet model at lepton collider

In this study, computational analysis of neutral Higgs bosons $h$, $H$ and $A$ is carried out within the parameter space of Two Higgs Doublet Model (2HDM) type-I in exact alignment limit of $\sin{(\beta - \alpha)} = 1$ at compact linear collider. Assuming Compact Linear Collider (CLIC) scenario where the electron-positron beams will be collided at $\sqrt{s}$ = 1.5 TeV. Two different values of predicted integrated luminosities are used in our calculations, 1000 $fb^{-1}$ and 2500 $fb^{-1}$. Three signal processes $e^+ e^- \rightarrow Zhh \rightarrow jjb\bar{b}b\bar{b}$, $e^+ e^- \rightarrow ZHH \rightarrow jjb\bar{b}b\bar{b}$ and $e^+ e^- \rightarrow Zhh \rightarrow jjb\bar{b}b\bar{b}$ are selected for analysis. The polarized colliding beams are used to enhance the signal production cross-section. Low $\tan{\beta}$ and equal Higgs masses regime is chosen in favor of Hadronic decay of $Z$ boson and $H \rightarrow b\bar{b}$. Different signal scenarios are selected and event generation is performed for each process separately. The $W$ and $Z$ boson, as well as top quark backgrounds are analyzed. Signal significance is computed at each Higgs mass hypothesis for three signal processes. After a comprehensive study, we did not find sizeable amount of signal events on top of the background but still, signal significance is found to be larger than 1, without taking into account the detector effects and systematics. The maximum calculated value of signal significance is observed to lie in the range of 150 $\leq$ $m_H$ $\leq$ 250 GeV for $Zhh$ while for $ZHH$ the range is 175 $\leq$ $m_H$ $\leq$ 200 GeV at 1000 $fb^{-1}$ and 175 $\leq$ $m_H$ $\leq$ 225 GeV region at 2500 $fb^{-1}$. Similarly, for $ZAA$ process, the significance is highest at $m_A$ = 175 GeV for both 1000 and 2500 $fb^{-1}$.