  The $R_{D^{(\ast)}}$ anomaly is one of the most intriguing experimental
results in particle physics today. Experiments such as BaBar, Belle and LHCb
have measured a consistent tension with the standard model (SM). We study
several extensions of the SM that could potentially explain this tension, such
as production of heavy $\mathrm{W}^{\prime}$ bosons, under the sequential SM
scenario, leptoquarks with preferential couplings to third generation fermions,
and interpretations through effective field theories. Such models, are not only
able to explain the $R_{D^{(\ast)}}$ anomaly but also to produce distinctive
signatures at the LHC. We present different feasibility studies to probe each
of these scenarios at the LHC, considering final states with one
$\mathrm{b}$-quark candidate, one hadronically decaying tau lepton ($\tau_{h}$)
and missing transverse momentum ($p^{miss}_{\mathrm{T}}$). The selection
criteria has been optimized for each model to achieve best signal signficance.
The studies are performed considering different LHC running conditions, at
$\sqrt{s} = 13 \, \mathrm{TeV}$ and 13.6 $\mathrm{TeV}$, and different
luminosities (150~$\mathrm{fb}^{-1}$ and 3000~$\mathrm{fb}^{-1}$).
