Slight excess at 130 GeV in search for a charged Higgs boson decaying to a charm quark and a bottom quark at the Large Hadron Collider

Searches for a charged Higgs boson ($H^\pm$) decaying to a charm quark and a bottom quark ($H^\pm \to cb$) have been carried out at the Large Hadron Collider (LHC) in the decay of top quarks ($t\to H^\pm b$). In a recent search by the ATLAS collaboration (with all Run II data, 139 fb$^{-1}$) a local excess of around $3\sigma$ has been observed, which is best fitted by a charged Higgs boson with a mass ($m_{H^\pm}$) of around 130 GeV and a product of branching ratios (BRs) given by BR$(t\to H^\pm b)\times{\rm BR}(H^\pm\to cb)=0.16\%\pm 0.06\%$. In the context of Two-Higgs-Doublet Models (2HDM) with independent Yukawa couplings for $H^\pm$ we present the parameter space for which this excess (assuming it to be genuine) can be accommodated, taking into account the limits from LHC searches for $H^\pm\to cs$ and $H^\pm\to \tau\nu$ at $m_{H^\pm}$=130 GeV and the constraint from $b\to s\gamma$. It is then shown that such an excess cannot be explained in 2HDMs with natural flavour conservation, but can be accommodated in the flipped Three-Higgs-Doublet Model (3HDM) and in the aligned 2HDM (A2HDM). Upcoming searches with 139 fb$^{-1}$ in the channels $H^\pm\to cb$ (CMS), $H^\pm \to cs$ (ATLAS/CMS) and $H^\pm \to \tau\nu$ (ATLAS/CMS) will determine if the excess is the first sign of an $H^\pm$ with $m_{H^\pm}=130$ GeV.