Using an Effective Charges Method to extract Lambda-MS-bar from event shape moments in e+e- annihilation

TL;DR

This paper evaluates the Effective Charges method for extracting the strong coupling constant from event shape moments in e+e- annihilation, finding NLO ECH performs better than standard MS-bar, but NNLO ECH and higher moments face challenges.

Contribution

It introduces a comparative analysis of ECH and MS-bar methods at different orders, highlighting the effectiveness of NLO ECH and issues at NNLO for event shape observables.

Findings

NLO ECH yields alpha_s(M_z)=0.1193±0.0003 from <1-T>

ECH at NNLO underperforms compared to NLO and struggles with higher moments

Small power corrections suffice at NLO, but models fail at NNLO

Abstract

We use an Effective Charges (ECH) method to extract Lambda-MS-bar, and hence alpha_s(M_z), from event shape moments in e+e- annihilation. We compare these results with ones obtained using standard MS-bar perturbation theory. The ECH method at NLO is found to perform better than standard MS-bar perturbation theory when applied to means of event shape observables. For example, when we apply the NLO ECH method to <1-T> we get alpha_s(M_z)=0.1193\pm0.0003. 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 beta-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-bar perturbation theory. Whilst only small power corrections are required when using ECH at NLO, it is found that these models are insufficient to couteract the undesirable behaviour of ECH at NNLO.