Leptonic Decay of Upsilon, a Possible Signature of New Physics

Abstract

We calculate the inclusive decay width of $Υ\to l^+ l^-$. Then we get the ratio $R_{τμ}=Γ[Υ\to τ^+τ^-]/ Γ[Υ\to μ^+μ^-]$ to ${\cal{O}}(α)$ and ${\cal{O}}(α_s^2)$ within the Standard Model(SM). Comparing with the recent Babar's data $R_{τμ}=1.005\pm0.013\pm 0.022$, we find that SM prediction $R_{τμ}$ is not consistent with the experimental data in the error bar. The discrepancy is about $1.25σ$. So leptonic decay of $Υ$ may be a possible signature of New Physics(NP). We present a better approach to test the Standard Model, $R_{τμ}(E_{soft})=.Γ[Υ\to τ^+τ^-+X]/ Γ[Υ\to μ^+μ^-+X]|_{E_X<E_{soft}}$. After resumming the large logarithms, we get $R_{τμ}(E_{soft})$ at the precision level of 0.1%. It can be compared with experimental data more precise. We also consider the impact of $R_{τμ}(E_{soft})$ and $R_{τμ}$ from light Higgs $h$ and pseudoscalar Higgs $A_0$.