Strong Coupling Constant from Scaling Violations in Fragmentation Functions

We present a new determination of the strong coupling constant ${\alpha }_s$ through the scaling violations in the fragmentation functions for charged pions, charged kaons, and protons. In our fit we include the latest $e^{+}{e}^{-}$ annihilation data from CERN LEP1 and SLAC SLC on the $Z$-boson resonance and older, yet very precise, data from SLAC PEP at center-of-mass energy $\sqrt{s}=29\mathrm{}\mathrm{GeV}$. At next-to-leading order, we find ${\alpha }_s^{\left(5\right)}\left(M_Z\right)=0.1170\mathrm{}\pm 0.0073$. A new world average of ${\alpha }_s$ is given.