A simultaneous measurement of the QCD colour factors and the strong coupling

Abstract.

Using data from $e^+e^-$ annihilation into hadrons, taken with the OPAL detector at LEP at the Z pole between 1991 and 1995, we performed a simultaneous measurement of the colour factors of the underlying gauge group of the strong interaction, $C_F$ and $C_A$, and the strong coupling, $\alpha_s$. The measurement was carried out by fitting next-to-leading order perturbative predictions to measured angular correlations of 4-jet events together with multi-jet related variables. Our results,

\[ C_A=3.02\pm 0.25\mathrm{(stat.)} \pm 0.49\mathrm{(syst.)}\:,\quad C_F=1.34\pm 0.13\mathrm{(stat.)} \pm 0.22\mathrm{(syst.)}\:, \]

\[ \alpha_s (M_Z)=0.120\pm 0.011\mathrm{(stat.)} \pm 0.020\mathrm{(syst.)}\:, \]

provide a test of perturbative QCD in which the only assumptions are non-abelian gauge symmetry and standard hadronization models. The measurements are in agreement with SU(3) expectations for $C_F$ and $C_A$ and the world average of $\alpha_s(M_{Z})$.