Leptonic Decay of Upsilon, a Possible Signature of New Physics

Abstract

We calculate the inclusive decay width of ${\rm Y}\to l^{+}{l}^{-}$. Then we get the ratio $R_{\tau \mu }=\Gamma [{\rm Y}\to {\tau }^{+}{\tau }^{-}]/\Gamma [{\rm Y}\to {\mu }^{+}{\mu }^{-}]$ to $\mathcal{O}(\alpha )$ and $\mathcal{O}({\alpha }_s^2)$ within the Standard Model(SM). Comparing with the recent Babar's data $R_{\tau \mu }=1.005\pm 0.013\pm 0.022$, we find that SM prediction $R_{\tau \mu }$ is not consistent with the experimental data in the error bar. The discrepancy is about $1.25\sigma$. So leptonic decay of ${\rm Y}$ may be a possible signature of New Physics(NP). We present a better approach to test the Standard Model, $R_{\tau \mu }(E_{soft})=.\Gamma [{\rm Y}\to {\tau }^{+}{\tau }^{-}+X]/\Gamma [{\rm Y}\to {\mu }^{+}{\mu }^{-}+X]{|}_{E_X<E_{soft}}$. 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 $R_{\tau \mu }$ from light Higgs $h$ and pseudoscalar Higgs $A_0$.

Comments: Comments are wellcome