  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.

High Energy Physics - Phenomenology;High Energy Physics - Experiment