Event Shape Data from e+e− annihilation into hadrons collected by the JADE experiment at centre-of-mass energies between 14 GeV and 44 GeV are used to determine the strong coupling αS. QCD predictions complete to next-to-next-to-leading order (NNLO), alternatively combined with resummed next-to-leading-log-approximation (NNLO + NLLA) calculations, are used. The combined value from six different event shape observables at the six JADE centre-of-mass energies using the NNLO calculations is $${array}{rcl} { {α S}( {m_{ { {Z⁰}}}})}&=&0.1210± 0.0007 {(stat.)}± 0.0021 {(exp.)}\\[6pt]&&{}± 0.0044 {(had.)}± 0.0036 {(theo.)}{array}$$ and with the NNLO + NLLA calculations the combined value is $${array}{rcl} { {α S}( {m_{ { {Z⁰}}}})}&=&0.1172± 0.0006 {(stat.)}± 0.0020 {(exp.)}\\[6pt]&&{}± 0.0035 {(had.)}± 0.0030 {(theo.)}.{array}$$ The stability of the NNLO and NNLO + NLLA results with respect to missing higher order contributions, studied by variations of the renormalisation scale, is improved compared to previous results obtained with NLO + NLLA or with NLO predictions only. The observed energy dependence of αS agrees with the QCD prediction of asymptotic freedom and excludes absence of running with 99% confidence level.
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Bethke et al. (2009) studied this question.