Using an Effective Charges Method to extract ΛMS¯ from event shape moments in e+e−e+e− annihilation

We use an Effective Charges (ECH) method to extract ΛMS¯, and hence αs(Mz)αs(Mz), from event shape moments in e+e−e+e− annihilation. We compare these results with ones obtained using standard MS¯ perturbation theory. The ECH method at NLO is found to perform better than standard MS¯ perturbation theory when applied to means of event shape observables. For example, when we apply the NLO ECH method to 〈1−T〉〈1−T〉 we get αs(Mz)=0.1193±0.0003αs(Mz)=0.1193±0.0003. However ECH at NNLO is found to work less well than ECH at NLO, and the ECH method also fails to describe data for higher moments of event shapes. We attempt to explain this by considering the ECH β  -function as an asymptotic series. We also examine the effect of adding two different models for non-perturbative power corrections to the perturbative approximation given by the ECH method and MS¯ perturbation theory. Whilst only small power corrections are required when using ECH at NLO, it is found that these models are insufficient to counteract the undesirable behaviour of ECH at NNLO.