A Precise Determination of \(\alpha_s\) From LEP Thrust Data Using Effective Field Theory

Abstract

Starting from a factorization theorem in Soft-Collinear Effective Theory, the thrust distribution in e\(^+\)e\(^-\) collisions is calculated including resummation of the next-to-next-to-next-to leading logarithms. This is a significant improvement over previous calculations which were only valid to next-to-leading logarithmic order. The fixed-order expansion of the resummed result approaches the exact fixed-order distribution towards the kinematic endpoint. This close agreement provides a verification of both the effective field theory expression and recently completed next-to-next-to-leading fixed order event shapes. The resummed distribution is then matched to fixed order, resulting in a distribution valid over a large range of thrust. A fit to ALEPH and OPAL data from LEP 1 and LEP 2 produces \(\alpha_s(m_Z\))= 0.1172 \(\pm\) 0.0010 \(\pm\) 0.0008 \(\pm\) 0.0012 \(\pm\) 0.0012, where the uncertainties are respectively statistical, systematic, hadronic, and perturbative. This is one of the world's most precise extractions of \(\alpha_s\) to date.