Coup de grace to the charged Higgs solution of $P_5^\prime$ and $R_{D^{(*)}}$ discrepancies

We consider a general two Higgs doublet model which can simultaneously solve discrepancies in neutral B meson decay ($b\to s\ell \overline \ell$ distribution) and charged B meson decay ($b\to c\tau\overline\nu$) with a charged Higgs. The model contains two additional neutral scalars at the same mass scale and predicts distinctive signals at the LHC. Based on the recent same-sign top search by the ATLAS collaboration, we found the constraint on the scalar mass spectrum. To probe the remaining mass window, we propose a novel $cg\to t\tau\overline\tau$ process at the LHC.