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 full next-to-next-to-next-to-leading logarithmic (${\mathrm{N}}^3\mathrm{LL}$) accuracy in QCD, also including the impact of next-order logarithmic corrections (${\mathrm{N}}^4\mathrm{LL}$). We consistently combine resummation with the known fixed-order results up to next-to-next-to-leading order (NNLO). All perturbative terms up to $\mathcal{O}({\alpha }_S^3)$ are included in our calculation, which, thanks to a unitarity constraint, exactly reproduces, after integration over $T$, the next-to-next-to-next-to-leading order (${\mathrm{N}}^3\mathrm{LO}$) result for the total cross section of $e^{+}{e}^{-}$ into hadrons. We perform resummation in the Laplace-conjugated space, which ensures the factorization of the kinematic momentum conservation constraint, and compare our results with those obtained using the resummation formalism in the physical ($T$) space. We find that the differences in the spectra obtained with the two different formalisms are sizable. Nonperturbative corrections are included using 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. We explicitly show that resumming Sudakov logarithms in Laplace-conjugated space and evaluating the inverse Laplace transform exactly is crucial in order to obtain an accurate determination of the QCD coupling.

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• Perturbative QCD
• QCD phenomenology
• Resummation methods