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 $\alpha_s(M_{Z})$ .
Highlights
Electron-positron annihilation into hadrons at high energies provides a precise means to test Quantum Chromodynamics (QCD), the theory of strong interactions
The DELPHI Collaboration [12] has performed a least-squares fit of leading order predictions to the two-dimensional distribution in the variables cos ΘNR and cos α34 in order to measure of the colour factor ratios
The ALEPH Collaboration [9] was the first to present a simultaneous measurement of the strong coupling and the colour factors
Summary
Electron-positron annihilation into hadrons at high energies provides a precise means to test Quantum Chromodynamics (QCD), the theory of strong interactions. Due to the purely leptonic initial state, there are many experimental quantities for which the long-distance (non-perturbative) effects are modest, especially when compared to similar quantities in hadron-hadron collisions or deep inelastic scattering. These quantities, for instance the total cross section and jet-related correlations, can be calculated in perturbative QCD as a function of a single parameter, the strong coupling strength, αs. The simultaneous measurement of the strong coupling and the eigenvalues of the quadratic Casimir operator of the underlying gauge theory, the CF and CA colour factors, provides a more general and comprehensive test of QCD than measurements of αs alone. A simultaneous fit of these parameters to data provides a means to investigate whether the data favour or exclude the additional degrees of freedom
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