$Υ$ and $ψ$ leptonic decays as probes of solutions to the $R_D^{(*)}$ puzzle
Experimental measurements of the ratios $R(D^{(*)})\equiv\frac{Γ(B\to D^{(*)}τν)}{Γ(B\to D^{(*)}\ellν)}$ ($\ell=e,μ$) show a $3.9σ$ deviation from the Standard Model prediction. In the absence of light right-handed neutrinos, a new physics contribution to $b\to cτν$ decays necessarily modifies also $b\bar b\toτ^+τ^-$ and/or $c\bar c\toτ^+τ^-$ transitions. These contributions lead to violation of lepton flavor universality in, respectively, $Υ$ and $ψ$ leptonic decays. We analyze the constraints resulting from measurements of the leptonic vector-meson decays on solutions to the $R(D^{(*)})$ puzzle. Available data from BaBar and Belle can already disfavor some of the new physics explanations of this anomaly. Further discrimination can be made by measuring $Υ(1S,2S,3S)\toττ$ in the upcoming Belle II experiment.