$R_{D^{(*)}}$ anomaly: A possible hint for natural supersymmetry with $R$-parity violation

Recently, several $B$-physics experiments have reported an appreciable deviation from the Standard Model (SM) in the tree-level observables $R_{D^{(*)}}$; the combined weighted average now stands at $\approx 4 \sigma$. We first show the anomaly necessarily implies model-independent collider signals of the form $pp \to b \tau \nu$ that should be expediously searched for at ATLAS/CMS as a complementary test of the anomaly. Next we suggest a possible interconnection of the anomaly with the radiative stability of the Standard Model Higgs boson and point to a minimal effective supersymmetric scenario with $R$-parity violation as the underlying cause. We also comment on the possibility of simultaneously explaining the recently reported $R_{K^{(*)}}$ anomaly in this setup.