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Addressing $R_{D^{(*)}}$, $R_{K^{(*)}}$, muon $g-2$ and ANITA anomalies in a minimal $R$-parity violating supersymmetric framework

We analyze the recent hints of lepton flavor universality violation in both charged-current and neutral-current rare decays of $B$-mesons in an $R$-parity violating supersymmetric scenario. Motivated by simplicity and minimality, we had earlier postulated the third-generation superpartners to be the lightest (calling the scenario "RPV3") and explicitly showed that it preserves gauge coupling unification and of course has the usual attribute of naturally addressing the Higgs radiative stability. Here we show that both $R_{D^{(*)}}$ and $R_{K^{(*)}}$ flavor anomalies can be addressed in this RPV3 framework. Interestingly, this scenario may also be able to accommodate two other seemingly disparate anomalies, namely, the longstanding discrepancy in the muon $(g-2)$, as well as the recent anomalous upgoing ultra-high energy ANITA events. Based on symmetry arguments, we consider three different benchmark points for the relevant RPV3 couplings and carve out the regions of parameter space where all (or some) of these anomalies can be simultaneously explained. We find it remarkable that such overlap regions exist, given the plethora of precision low-energy and high-energy experimental constraints on the minimal model parameter space. The third-generation superpartners needed in this theoretical construction are all in the 1-10 TeV range, accessible at the LHC and/or next-generation hadron collider. We also discuss some testable predictions for the lepton-flavor-violating decays of the tau-lepton and $B$-mesons for the current and future $B$-physics experiments, such as LHCb and Belle II. Complementary tests of the flavor anomalies in the high-$p_T$ regime in collider experiments such as the LHC are also discussed.