Correlation between the scaling factor of the yukawa coupling and cross section for the $e^+ e^- \rightarrow hhf\overline{f}$ ($f\neq t$) in type-I 2HD
The objective of this study is to correlate the scaling factor of the Standard Model (SM) like Higgs boson and the cross section ratio of the process $e^+ e^- \rightarrow hhf\overline{f}$ where $f\neq t$, normalized to SM predictions in the type I of the Two Higgs Doublet Model. All calculations have been performed at $\sqrt{s}=500$ GeV and $1 \leq \tanβ \leq 30$ for masses $m_H = m_A = m_{H^\pm} = 300GeV$ and $m_H=300$ GeV, $m_A=m_{H^\pm}=500$ GeV. The working scenario is by taking without alignment limit, that is $s_{β-α}= 0.98$ and $s_{β-α}= 0.99,$ $0.995$, which gives the enhancement in the cross section, particularly a few times greater than the predictions of the SM due to resonant-impacts of the additional heavy neutral Higgs bosons. This shows that enhancement in cross section occurs on leaving the alignment i.e., $s_{β-α}=1$, at which all the higgs that couple to vector bosons and fermions have the same values as in SM at tree level. A large value of enhancement factor is obtained at $s_{β-α}= 0.98$ compared to $s_{β-α}= 0.99,$ $0 .995$. Furthermore, the decrease in the enhancement factor is observed for the case when $m_H=300$ GeV, $m_A=m_{H^\pm}=500$ GeV. The behavior of the scaling factor with $\tanβ$ is also studied, which shows that for large values of $\tanβ$, the scaling factor becomes equal to $s_{β-α}$. Finally a convincing correlation is achieved by taking into account, the experimental and theoretical constraints e.g, perturbative unitarity, vacuum stability and electroweak oblique parameters.