The two Higgs doublet type-II seesaw model: Naturalness and $\bar{B}\to X_s{\hat{I}}^3$ versus heavy Higgs masses

Abstract

We extend the work \cite{Ouazghour:2018mld} to a more general and detailed analysis through studying the naturalness problem and $B$ physics constraints within the context of two higgs doublets model augmented with a complex scalar triplet field ($2HDMcT$). We first derive the modified Vetman conditions and show that naturalness problem might be evaded at the electroweak scale. Then, we evaluate the branching ratio of $\bar{B}\to X_s{\hat{I}}^3$ radiative decay at the Next to leading order. Besides unitarity, boundedness from below constraints and the present collider data from Higgs signal rate measurements, the parameter space of $2HDMcT$ is then revisited to see how the modified Veltman conditions and $\bar{B}\to X_s{\hat{I}}^3$ experimental bounds induce significant delimitations. Our analysis shows that the naturalness affects drastically the masses of heavy Higgs $h_3$, $A_2$, $H_2^{\pm }$ and $H^{\pm \pm }$. More specifically, we considered three benchmak scenarios corresponding to $\hat{I}{¼}_2>20,40,70$ GeV. For $\hat{I}{¼}_2>40$, we find stringent upper limits on $m_{h_2}$, $m_{A_1}$ and $m_{H_1^{\pm }}$ at $880$, $920$ and $918$ GeV respectively. If, in addition, the measurements of $\bar{B}\to X_s{\hat{I}}^3$ decay rate are also considered, the lower masses limits of nonstandard Higgs bosons ($h_2$, $h_3$, $A_1$, $A_2$, $H_1^{\pm }$, $H_2^{\pm }$, $H^{\pm \pm }$) are pushed up to higher values located between $490$ and $750$ GeV. Besides, we also demonstrate that the $\bar{B}\to X_s{\hat{I}}^3$ experimental limits can only be accommodated within $2HDMcT$ if two conditions are fullfilled : $\hat{I}{\pm }_1$ parameter positive and the Higgs mass hierarchy $m_{h_3}>m_{H_2^{\pm }}>m_{H^{\pm \pm }}$.

9 pages, 4 figures, LaTeX. Accepted in Physics Letters B