Coupling constant in dispersive model

Abstract

The average of the moments for event shapes in e ⁺ e− →hadrons within the context of next-to-leading order (NLO) perturbative QCD prediction in dispersive model is studied. Moments used in this article are $\langle {1-T}\rangle$, $\langle \rho\rangle$, $\langle {B_{\rm T}}\rangle$ and $\langle {B_{\rm W} }\rangle$. We extract α _s, the coupling constant in perturbative theory and α ₀ in the non-perturbative theory using the dispersive model. By fitting the experimental data, the values of $\alpha_{\rm s} ({M_{\rm Z^0} })=0.1171\pm 0.00229$ and $\alpha_0 \left( {\mu_{\rm I} =2\,{\rm GeV}} \right)=0.5068\pm 0.0440$ are found. Our results are consistent with the above model. Our results are also consistent with those obtained from other experiments at different energies. All these features are explained in this paper.