${\alpha }_s$ determination at NNLO${}^{\star }$+NNLL accuracy from the energy evolution of jet fragmentation functions at low $z$

The QCD coupling ${\alpha }_s$ is extracted from the energy evolution of the first two moments (multiplicity and mean) of the parton-to-hadron fragmentation functions at low fractional hadron momentum $z$. Comparisons of the experimental $e^{+}{e}^{-}$ and deep-inelastic $e^{\pm }$p jet data to our NNLO${}^{\ast }$+NNLL predictions, allow us to obtain ${\alpha }_s(m_{{}_{\mathrm{Z}}})$ = 0.1205$\pm$0.0010${}_{-0.0000}^{+0.0022}$, in excellent agreement with the current world average determined using other methods at the same level of accuracy.