Measurement of the Direct Photon Spectrum in $\Upsilon(1S)$ Decays

TL;DR

This paper measures the direct photon spectrum in $(1S)$ decays to determine the ratio of radiative to hadronic decay widths, leading to an extraction of the strong coupling constant and QCD scale parameter.

Contribution

It provides a precise measurement of the photon emission ratio in $(1S)$ decays and derives fundamental QCD parameters from experimental data.

Findings

Measured $R_{ ext{gamma}}$ as (2.75 ± 0.04(stat.) ± 0.15(syst.))%.

Determined $_{ ext{MS}}$ as 233 ± 11 ± 59 MeV.

Calculated $_{s}(M_{Z})$ as 0.110 ± 0.001 ± 0.007.

Abstract

Using data taken with the CLEO II detector at the Cornell Electron Storage Ring, we have determined the ratio of branching fractions: $R_{\gamma} \equiv \Gamma(\Upsilon(1S) \rightarrow \gamma gg)/\Gamma(\Upsilon(1S) \rightarrow ggg) = (2.75 \pm 0.04(stat.) \pm 0.15(syst.))%$. From this ratio, we have determined the QCD scale parameter $\Lambda_{\overline{MS}}$ (defined in the modified minimal subtraction scheme) to be $\Lambda_{\overline{MS}}= 233 \pm 11 \pm 59$ MeV, from which we determine a value for the strong coupling constant $\alpha_{s}(M_{\Upsilon(1S)}) = 0.163 \pm 0.002 \pm 0.014$, or $\alpha_{s}(M_{Z}) = 0.110 \pm 0.001 \pm 0.007$.