Correlated enhancements in $D_s \to \ellν$, $(g-2)$ of muon, and lepton flavor violating $τ$ decays with two R-parity violating couplings

Abstract

With just two R-parity violating couplings, $λ'_{223}$ and $λ'_{323}$, we correlate several channels, namely, $D_s \to \ell ν$ ($\ell = μ, τ$), $(g-2)_μ$, and some lepton flavor violating $τ$ decays. For $λ'_{223} = λ'_{323} \sim 0.3$ 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: ${\rm Br} (τ\to μγ) \sim 4.5 \cdot 10^{-8}$, ${\rm Br} (τ\to μμμ) \sim 1.2 \cdot 10^{-8}$, ${\rm Br} (τ\to μη/η') \sim 4 \cdot 10^{-10}$, and $(g_μ-2)/2 \sim 4 \cdot 10^{-11}$. We exhibit our results through observable versus observable correlation plots.