$H^\pm\to cb$ in models with two or more Higgs doublets

Searches for light $H^\pm$s via $t\to H^\pm b$ are being carried out at the LHC. Herein, it is normally assumed that the dominant decay channels are $H^\pm\to \tau\nu$ and $H^\pm\to cs$ and separate data analyses are performed with comparable sensitivity to the underlying model assumptions. However, the $H^\pm\to cb$ decay rate can be as large as $80\%$ in models with two or more Higgs doublets with natural flavour conservation, while satisfying the constraint from $b\to s\gamma$ for $m_{H^\pm}< m_t$. Despite the current search strategy for $H^\pm\to cs$ is also sensitive to $H^\pm\to cb$, a significant gain in sensitivity could be obtained by tagging the $b$ quark from the decay $H^\pm\to cb$.