Mearsurement of $\alpha_s$ and the $\beta$ function with the DELPHI detector at LEP

Abstract

Event shape distributions in $e^+e^-$ annihilation are determined from the DELPHI data taken between 183 and 207\gev. From these the strong coupling $\alpha_s$ is extracted with several techniques. Together with the results from other LEP2 energies and at about $m_Z$ this allows both, a combined measurement of $\alpha_s$ and a test of the scale dependence of the strong interaction. Alternatively the renormalisation group invariant (RGI) perturbation theory is applied to measure the $\beta$ function of strong interaction. The results are good agreement with the QCD expectation and allow to exclude the existence of light gluinos with a mass below 30\gev in a model independent way.