Searching for a charged Higgs boson with both $H^{pm}W^{mp}Z$ and $H^{pm}tb$ couplings at the LHC

In certain new physics scenarios, a singly charged Higgs boson can couple to both fermions and $W^pm Z$ at tree level. We develop new strategies beyond current experimental searches using $ppto jjH^pm$, $H^pm to tb $ at the Large Hadron Collider (LHC). With the effective $H^pm W^mp Z$ and $H^pm tb$ couplings we perform a model-independent analysis at the collision energy $sqrt{s}=13$~TeV with the integrated luminosity of $3~text{ab}^{-1}$. We derive the discovery prospects and exclusion limits for the charged Higgs boson in the mass range from 200~GeV to 1~TeV. With $|F_{WZ}|,|A_t|sim 0.5-1.0$ and $300~text{GeV}lesssim m_{H^pm}lesssim 400~text{GeV}$, we point out that a discovery significance of $5sigma$ can be achieved. The constraints and projected sensitivities are also discussed in a realistic model, i.e., the modified Georgi-Machacek model without custodial symmetry. Our proposed search would provide direct evidence for a charged Higgs boson $H^pm$ that couples to $W^pm Z$ and $tb$, which can have better sensitivity to the couplings of $H^pm W^mp Z$ and $H^pm tb$ than current searches.