Hints of Natural Supersymmetry in Flavor Anomalies?

The recent results from the Fermilab muon $g-2$ experiment, as well as the persisting hints of lepton flavor universality violation in $B$-meson decays, present a very strong case for flavor-nonuniversal new physics beyond the Standard Model. We assert that a minimal $R$-parity violating supersymmetric scenario with relatively light third-generation sfermions (dubbed as 'RPV3') provides a natural, well-motivated framework for the simultaneous explanation of all flavor anomalies, while being consistent with a multitude of low-energy flavor constraints, as well as with limits from high-energy collider searches. We further propose complementary tests and distinct signatures of this scenario in the high-$p_T$ searches at current and future colliders. Specifically, we find that an sbottom in the mass range of 2-12 TeV accounts for $R_{D^{(*)}}$ and $R_{K^{(*)}}$ flavor anomalies and it only plays a minor role in the $(g-2)_\mu$ anomaly, whereas a sneutrino with mass between 0.7-1 TeV is the dominant player for $(g-2)_\mu$. In this context, we propose specific collider signatures of sbottom via its decays to $ \overline{ t}(t) \mu^+ \mu^-$, and of sneutrino pairs with their decays leading to a highly distinctive and spectacular four-muon final state, which can be used to completely probe the RPV3 parameter space of interest.