Leptonic Decay of Upsilon, a Possible Signature of New Physics

We calculate the inclusive decay width of $\mathrm{{\rm Y}}\to l^{+}{l}^{-}$. Then we get the ratio $R_{\tau\mu}=\Gamma[\Upsilon \to \tau^+\tau^-]/ \Gamma[\Upsilon \to \mu^+\mu^-]$to${\cal{O}}(\alpha)$and${\cal{O}}(\alpha_s^2)$ within the Standard Model(SM). Comparing with the recent Babar’s data $R_{\tau \mu}=1.005\pm0.013\pm 0.022$,wefindthatSMprediction$R_{\tau\mu}$ is not consistent with the experimental data in the error bar. The discrepancy is about $1.25\sigma$. So leptonic decay of $\mathrm{{\rm Y}}$ may be a possible signature of New Physics(NP). We present a better approach to test the Standard Model, $R_{\tau\mu}(E_{soft})=.\Gamma[\Upsilon \to \tau^+\tau^-+X]/ \Gamma[\Upsilon \to \mu^+\mu^-+X]|{E_X<E{soft}}$. After resumming the large logarithms, we get $R_{\tau \mu }(E_{soft})$ at the precision level of 0.1%. It can be compared with experimental data more precise. We also consider the impact of $R_{\tau \mu}(E_{soft})$and$R_{\tau \mu}$fromlightHiggs$h$andpseudoscalarHiggs$A_0$.