Leptonic Decay of Upsilon, a Possible Signature of New Physics

TL;DR

This paper calculates the decay ratio of Upsilon into tau and muon pairs within the Standard Model, finds a slight discrepancy with experimental data suggesting possible new physics, and proposes a refined test method for future experiments.

Contribution

It provides a detailed Standard Model prediction for the leptonic decay ratio of Upsilon and introduces an improved approach to test for new physics effects in these decays.

Findings

Standard Model prediction of R_{τμ} is about 1.25σ away from experimental data.

Proposes a refined ratio R_{τμ}(E_{soft}) with 0.1% precision for better experimental comparison.

Considers effects of light Higgs and pseudoscalar Higgs on decay ratios.

Abstract

We calculate the inclusive decay width of $\Upsilon \to l^+ l^-$. 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 $R_{\tau \mu}=1.005\pm0.013\pm 0.022$, 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 $\Upsilon$ 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 $R_{\tau \mu}$ from light Higgs $h$ and pseudoscalar Higgs $A_0$.