Mearsurement of $α_s$ and the $β$ function with the DELPHI detector at LEP

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Event shape distributions in $e^+e^-$ annihilation are determined from the DELPHI data taken between 183 and 207\gev. From these the strong coupling $α_s$ 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 $α_s$ and a test of the scale dependence of the strong interaction. Alternatively the renormalisation group invariant (RGI) perturbation theory is applied to measure the $β$ 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.
Talk presented at the QCD02 conference, Montpellier 2002

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