Thrust distribution in electron-positron annihilation at full NNNLL+NNLO (and beyond) in QCD

Abstract

We consider the thrust ($T$) distribution in electron-positron ($e^{+}{e}^{-}$) annihilation into hadrons and we perform the all-order resummation of the large logarithms of $1-T$ up to next-to-next-to-next-to-next-to-leading logarithmic (N${}^4$LL) accuracy in QCD. We consistently combine resummed predictions with the known fixed-order results up to next-to-next-to-leading order (NNLO). All perturbative terms up to order ${\alpha }_S^3$ are included in our calculation which, thanks to a unitarity constraint, exactly reproduce after integration over the variable $T$ the next-to-next-to-next-to-leading order (N${}^3$LO) result for the total cross section of $e^{+}{e}^{-}$ into hadrons. We resum the large logarithms in the Laplace-conjugated space and compare our results with those obtained with the analytic resummation formalism in the physical ($T$) space. We find that the differences in the spectra obtained with the two different formalisms are sizable. Non-perturbative corrections have been included through an analytic hadronization model depending on two free parameters. Finally, we present a comparison of our spectra with experimental data at the $Z$-boson mass ($m_Z$) energy, which enables us to extract the value of the QCD coupling ${\alpha }_S(m_Z^2)=0.1181\pm 0.0018$ fully consistent with the world average.

Comments: 16 pages, 2 figures. Minor corrections, added references, results unchanged. Version submitted to journal