Two-Higgs-Doublet type-II and -III models and $t\to ch$ at the LHC

We study the constraints of the generic two-Higgs-doublet model (2HDM) type-III and the impacts of the new Yukawa couplings. For comparisons, we revisit the analysis in the 2HDM type-II. To understand the influence of all involving free parameters and to realize their correlations, we employ $\chi$-square fitting approach by including theoretical and experimental constraints, such as S, T, and U oblique parameters, the production of standard model Higgs and its decay to $\gamma \gamma$, $W{W}^{\ast }\mathrm{/}Z{Z}^{\ast }$, ${\tau }^{+}{\tau }^{-}$, etc. The errors of analysis are taken at $68\mathrm{\%}$, $95.5\mathrm{\%}$, and $99.7\mathrm{\%}$ confidence levels. Due to the new Yukawa couplings being associated with $\cos (\beta -\alpha )$ and $\sin (\beta -\alpha )$, we find that the allowed regions for $\sin \alpha$ and $\tan \beta$ in the type-III model can be broader when the dictated parameter ${\chi }_F$ is positive; however, for negative ${\chi }_F$, the limits are stricter than those in the type-II model. By using the constrained parameters, we find that the deviation from the SM in the $h\to Z\gamma$canbeof${\cal O}(10%)$. Additionally, we also study the top-quark flavor-changing processes induced at the tree level in the type-III model and find that when all current experimental data are considered, we get $Br(t\to c(h, H) )< 10^{-3}$for$m_h=125.36$and$m_H=150$GeVand$Br(t\to cA)$slightlyexceeds$10^{-3}$for$m_A =130$ GeV.