Search for a light-charged Higgs in a two-Higgs-doublet type II seesaw model at the LHC
A charged Higgs in the type II two-Higgs-doublet model (THDM) has been bounded to be above a few hundred GeV by the radiative $B$ decays. A Higgs triplet extension of the THDM not only provides an origin of neutrino masses and a completely new doubly-charged Higgs decay pattern, but it also achieves a light-charged Higgs with a mass of ${\cal O}(100)$ GeV through the new scalar couplings in the scalar potential. It was found that these light-charged Higgs decays depend on its mass $m_{H^\pm}$, $\tan\beta$, and mixing effect $\sin\theta_\pm$: at $\tan\beta =1$, if $m_{H^\pm} > m_W + m_Z$, $\bar b b W^\pm$, $W^\pm Z$, and $\tau \nu$ are the main decay modes; however, if $m_{H^\pm} < m_W + m_Z$, the main decay modes are then $\bar b b W$ and $\tau \nu$, and at $\tan\beta=30$, the $\tau \nu$ mode dominates the other decays. When $m_t > m_{H^\pm} + m_b$, we found that the ATLAS and CMS recent upper bounds on the product of $BR(t\to H^+ b)BR(H^+\to \tau^+ \nu)$ can be directly applied and will give a strict constraint on the correlation of $m_{H^\pm}$ and $\sin\theta_\pm$. If the upper bound of $BR(t\to H^+ b)BR(H^+\to \tau^+ \nu)$ is satisfied (escaped) for $m_t > (<) m_{H^\pm} + m_b$, it was found that the significance of discovering the charged Higgs through $H^\pm \to W^\pm Z$ is much lower than that through $H^\pm \to \bar b b W^\pm$. With a luminosity of 100 fb$^{-1}$ at $\sqrt{s}=13$ TeV and including the experimental bounds, the significance of the $H^\pm \to \bar b b W^\pm$ signal can reach around $6.2 (2.4)\sigma$ for $m_{H^\pm} <(>) m_W + m_Z$.