A Study of Event Shapes and Determinations of $\alpha_s$ using data of $e^{+}e^{-}$ Annihilations at $\sqrt{s}$ = 22 to 44 GeV

Data recorded by the JADE experiment at the PETRA $e^+e^-$ collider were used to measure the event shape observables thrust, heavy jet mass, wide and total jet broadening and the differential 2-jet rate in the Durham scheme. For the latter three observables, no experimental results have previously been presented at these energies. The distributions were compared with resummed QCD calulations ($O(\alpha_s^2)$+NLLA), and the strong coupling constant results, \alpha_s(22 GeV) = 0.161 ^{+0.016}_{-0.011}, \alpha_s(35 GeV) = 0.143 ^{+0.011}_{-0.007}, \alpha_s(44 GeV) = 0.137 ^{+0.010}_{-0.007}, are in agreement with previous combined results of PETRA albeit with smaller uncertainties. Together with corresponding data from LEP, the energy dependence of $\alpha_s$ is significantly tested and is found to be in good agreement with the QCD expectation. Similarly, mean values of the observables were compared to analytic QCD predictions where hadronisation effects are absorbed in calculable power corrections.Data recorded by the JADE experiment at the PETRA e^+e^- collider were used to measure the event shape observables thrust, heavy jet mass, wide and total jet broadening and the differential 2-jet rate in the Durham scheme. For the latter three observables, no experimental results have previously been presented at these energies. The distributions were compared with resummed QCD calulations (O(alpha_s^2)+NLLA), and the strong coupling constant alpha_s(Q) was determined at different energy scales Q=sqrt{s}. The results, \alpha_s(22 GeV) = 0.161 ^{+0.016}_{-0.011}, \alpha_s(35 GeV) = 0.143 ^{+0.011}_{-0.007}, \alpha_s(44 GeV) = 0.137 ^{+0.010}_{-0.007}, are in agreement with previous combined results of PETRA albeit with smaller uncertainties. Together with corresponding data from LEP, the energy dependence of alpha_s is significantly tested and is found to be in good agreement with the QCD expectation. Similarly, mean values of the observables were compared to analytic QCD predictions where hadronisation effects are absorbed in calculable power corrections