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

TL;DR

This study investigates how the Higgs boson coupling scaling factor affects the cross section of a specific process in the type-I Two Higgs Doublet Model, revealing significant enhancements when deviating from the alignment limit.

Contribution

It provides a detailed analysis of the correlation between the Higgs coupling scaling factor and the cross section in the type-I 2HD model at different parameters, including resonance effects and constraints.

Findings

Cross section is significantly enhanced near the non-alignment limit.

The enhancement factor decreases with increasing Higgs masses.

The scaling factor aligns with $s_{\beta-\alpha}$ at large $\tan\beta$.

Abstract

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 $1 \leq \tan{\beta} \leq 30$ 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 $s_{\beta-\alpha}= 0.98$ and $s_{\beta-\alpha}= 0.99,$ $0.995$, 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., $s_{\beta-\alpha}=1$, 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 $s_{\beta-\alpha}= 0.98$ compared to $s_{\beta-\alpha}= 0.99,$ $0 .995$. 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 $\tan{\beta}$ is also studied, which shows that for large values of $\tan\beta$, the scaling factor becomes equal to $s_{\beta-\alpha}$. 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.