Correlated enhancements in $D_s \to \ell\nu$, $(g-2)$ of muon, and lepton flavor violating $\tau$ decays with two R-parity violating couplings
With just two R-parity violating couplings, $\lambda'_{223}$ and $\lambda'_{323}$, we correlate several channels, namely, $D_s \to \ell \nu$ ($\ell = \mu, \tau$), $(g-2)_\mu$, and some lepton flavor violating $\tau$ decays. For $\lambda'_{223} = \lambda'_{323} \sim 0.3$ and for a common superpartner mass of 300 GeV, which explain the recently observed excesses in the above $D_s$ decay channels, we predict the following R-parity violating contributions: ${\rm Br} (\tau \to \mu \gamma) \sim 4.5 \cdot 10^{-8}$, ${\rm Br} (\tau \to \mu\mu\mu) \sim 1.2 \cdot 10^{-8}$, ${\rm Br} (\tau \to \mu\eta/\eta') \sim 4 \cdot 10^{-10}$, and $(g_\mu-2)/2 \sim 4 \cdot 10^{-11}$. We exhibit our results through observable versus observable correlation plots.