Deep inelastic e^+ scattering data, taken with the H1 detector at HERA, are used to study the event shape variables thrust, jet broadening and jet mass in the current hemisphere of the Breit frame over a large range of momentum transfers Q between 7 GeV and 100 GeV. The data are compared with results from e^+e^- experiments. Using second order QCD calculations and an approach to relate hadronisation effects to power corrections an analysis of the Q dependences of the means of the event shape parameters is presented, from which both the power corrections and the strong coupling constant are determined without any assumption on fragmentation models. The power corrections of all event shape variables investigated follow a 1/Q behaviour and can be described by a common parameter alpha_0.
Jet event rates in deep inelastic ep scattering at HERA are investigated applying the modified JADE jet algorithm. The analysis uses data taken with the H1 detector in 1994 and 1995. The data are corrected for detector and hadronization effects and then compared with perturbative QCD predictions using next-to-leading order calculations. The strong coupling constant alpha_S(M_Z^2) is determined evaluating the jet event rates. Values of alpha_S(Q^2) are extracted in four different bins of the negative squared momentum transfer~$\qq$ in the range from 40 GeV2 to 4000 GeV2. A combined fit of the renormalization group equation to these several alpha_S(Q^2) values results in alpha_S(M_Z^2) = 0.117+-0.003(stat)+0.009-0.013(syst)+0.006(jet algorithm).
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