A Measurement of the QCD Colour Factors using Event Shape Distributions at sqrt(s)=14 GeV to 189 GeV

TL;DR

The paper probes the QCD gauge structure by extracting colour factors n_f, C_A, and C_F from event-shape distributions in e+e- annihilation across 14–189 GeV. It combines O(α_s^2) perturbative QCD with NLLA resummation and analytic power corrections (DMW model) to model hadronisation, allowing colour-factor variations while mitigating model dependence. Two- and multi-parameter fits to distributions of 1−T, C, B_T, and B_W yield results consistent with SU(3) (n_f ≈ 5, C_A ≈ 3, C_F ≈ 4/3), with final combined values: n_f = 5.64 ± 1.35, C_A = 2.88 ± 0.27, C_F = 1.45 ± 0.27; simultaneous fits give C_A = 2.84 ± 0.24 and C_F = 1.29 ± 0.18. These findings support the standard QCD gauge group and validate the power-correction framework for hadronisation in event-shape analyses, while noting reduced reliability for B_T and B_W predictions. The analysis also demonstrates that allowing α_0 to float reduces hadronisation uncertainties in colour-factor extractions. Overall, the work provides a competitive, complementary test of QCD’s gauge structure using energy-dependent event-shape data and analytic non-perturbative corrections.

Abstract

Measurements of the QCD colour factors C_A and C_F and of the number of active quark flavours n_f in the process e+e- -> hadrons at high energy are presented. They are based on fits of O(alpha_S**2)+NLLA QCD calculations to distributions of the event shape observables 1-T, C, B_T and B_W measured at centre-of-mass energies from 14 GeV to 189 GeV. Hadronisation effects are approximated with power correction calculations which also depend on the QCD gauge structure. In this approach potential biases from hadronisation models are reduced. Our results for individually measured quantities are n_f = 5.64 +- 1.35, C_A = 2.88 +- 0.27 and C_F = 1.45 +- 0.27 in good agreement with QCD based on the SU(3) symmetry group where n_f=5 for the energies considered here, C_A=3 and C_F=4/3. From simultaneous fits of C_A and C_F we find C_A = 2.84 +- 0.24 and C_F = 1.29 +- 0.18, which is also in good agreement with the QCD expectation.

Figures (4)

• Figure 1: The figures present results of fits to $\alpha_s(M_{\mathrm{Z^0}})$ and one of the colour factors $n_f$, $C_A$ or $C_F$ with observables as given on the vertical axis. The vertical dotted lines indicate the expectation from standard QCD for the colour factor.
• Figure 2: The figure presents results from fits to $\alpha_s(M_{\mathrm{Z^0}})$ and the colour factors $C_A$ and $C_F$ with observables as given on the vertical axis. The error bars show total uncertainties. The vertical dotted lines indicate the expectations from standard QCD for the colour factors.
• Figure 3: The figures present results from fits to $\alpha_s(M_{\mathrm{Z^0}})$, $\alpha_0$ and one of the colour factors $n_f$, $C_A$ or $C_F$ with observables as given on the vertical axis. The error bars show total uncertainties. The vertical dotted lines indicate the expectation from standard QCD for the colour factor.
• Figure 4: The figure presents the combined results for the colour factors $C_A$ and $C_F$ from fits to $\alpha_s(M_{\mathrm{Z^0}})$, $C_A$ and $C_F$ based on the observables $1-T$ and $C$. The square and triangle symbols indicate the expectations for $C_A$ and $C_F$ for different symmetry groups.