Measurement of the energy dependence of hadronic jet rates and the   strong coupling alpha_s from the four-jet rate with the DELPHI detector at   LEP
  Hadronic events from the data collected with the DELPHI detector at LEP within the energy range from 89 GeV to 209 GeV are selected, their jet rates are determined and compared to predictions of four different event generators. One of them is the recently developed APACIC++ generator which performs a massive matrix element calculation matched to a parton shower followed by string fragmentation. The four-jet rate is used to measure alpha_s in the next-to-leading-order approximation yielding alpha_s(M_Z^2) = 0.1175 +/- 0.0030. The running of alpha_s determined by using four-jet events has been tested. The logarithmic energy slope is measured to be d\alpha_s^{-1} / d\log E_{cm} = 1.14 +/- 0.36. Since the analysis is based on four-jet final states it represents an alternative approach to previous DELPHI alpha_s measurements using event shape distributions. 
The DELPHI Collaboration: J. Abdallah, et al