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

Abstract

With just two R-parity violating couplings, ${\lambda }_{223}^{\prime }$ and ${\lambda }_{323}^{\prime }$, we correlate several channels, namely, $D_s\to \ell \nu$ ($\ell =\mu ,\tau$), $(g-2{)}_{\mu }$, and some lepton flavor violating $\tau$ decays. For ${\lambda }_{223}^{\prime }={\lambda }_{323}^{\prime }\sim 0.3$ 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: $\mathrm{Br}(\tau \to \mu \gamma )\sim 4.5\cdot 10^{-8}$, $\mathrm{Br}(\tau \to \mu \mu \mu )\sim 1.2\cdot 10^{-8}$, $\mathrm{Br}(\tau \to \mu \eta /{\eta }^{\prime })\sim 4\cdot 10^{-10}$, and $(g_{\mu }-2)/2\sim 4\cdot 10^{-11}$. We exhibit our results through observable versus observable correlation plots.

Comments: 12 pages, 8 figures: v2: An equation and a few comments and references added, version to appear in Nucl Phys B