Particle multiplicity of unbiased gluon jets from e⁺e⁻ three-jet events

Abstract.

The charged particle multiplicities of two- and three-jet events from the reaction e$^+$e$^-$ $\rightarrow$ Z$^0\rightarrow hadrons$ are measured for Z$^0$ decays to light quark (uds) flavors. Using recent theoretical expressions to account for biases from event selection, results corresponding to unbiased gluon jets are extracted over a range of jet energies from about 11 to 30 GeV. We find consistency between these results and direct measurements of unbiased gluon jet multiplicity from $\Upsilon$ and Z$^0$ decays. The unbiased gluon jet data including the direct measurements are compared to corresponding results for quark jets. We perform fits based on analytic expressions for particle multiplicity in jets to determine the ratio $r\equiv\mathrm{N}_{g}/\mathrm{N}_{q}$ of multiplicities between gluon and quark jets as a function of energy. We also determine the ratio of slopes, $r^{(1)}\equiv(\mathrm{d}\mathrm{N}_{g} /\mathrm{d}y) /(\mathrm{d}\mathrm{N}_{q} /\mathrm{d}y)$, and of curvatures, $r^{(2)}\equiv(\mathrm{d}^2\mathrm{N}_{g} /\mathrm{d}y^2) /(\mathrm{d}^2\mathrm{N}_{q} /\mathrm{d}y^2)$, where y specifies the energy scale. At 30 GeV, we find $r=1.422\pm0.051,r^{(1)}=1.761\pm0.071$ and $r^{(2)}=1.98\pm0.13$, where the uncertainties are the statistical and systematic terms added in quadrature. These results are in general agreement with theoretical predictions. In addition, we use the measurements of the energy dependence of ${\mathrm{N}}_{g}$ and ${\mathrm{N}}_{q}$ to determine an effective value of the ratio of QCD color factors, $C_{\mathrm A}/C_{\mathrm F}$. Our result, $C_{\mathrm A}/C_{\mathrm F}=2.23\pm0.14$(total), is consistent with the QCD value of 2.25.