Towards ruling out the charged Higgs interpretation of the $R_{D^{(*)}}$ anomaly

Motivated by the notorious anomaly in the lepton flavor universality ratios $R_{D^{(*)}}$, we study the sensitivity of the Large Hadron Collider (LHC) to a low-mass charged Higgs boson $H^-$ lighter than $400\,$GeV in a generic two Higgs doublet model. A combination of current constraints from the $B_c\to\tau \nu$ decay, $B_{s}$ meson mixing data, tau sleptons and di-jet searches at the LHC allows to explain the $R_{D^{(*)}}$ anomaly at the $1\,\sigma$ level by a low-mass charged Higgs. In this context, we estimate the reach of an LHC search for resonant $H^-$ production, where the final state contains an energetic $\tau$ lepton decaying hadronically, a neutrino with large transverse momentum, and an additional $b$-jet ($pp \to b+\tau_h + \nu$). Requiring the additional $b$-tagged jet in the $\tau\nu$ resonance search profits from the suppression of the Standard Model background, and therefore it allows us to judge the low-mass $H^-$ interpretation of the $R_{D^{(*)}}$ anomaly. To demonstrate this, we perform a fast collider simulation for the $\tau \nu$ resonance search with an additional $b$-tagged jet, and find that most of the interesting parameter region of the whole mass range can already be probed with the current integrated luminosity of $139\,$fb$^{-1}$.