Experimental momentum spectra of identified hadrons at $e^+e^-$ colliders compared to QCD calculations

Experimental data on the shape of hadronic momentum spectra are compared to theoretical predictions in the context of calculations in the Modified Leading Log Approximation (MLLA), under the assumption of Local Parton Hadron Duality (LPHD). Considered are experimental measurements at $e^+e^-$-colliders of $\xi_p^*$, the position of the maximum in the distribution of $\xi_p=\log(1/x_p)$, where $x_p=p/p_{beam}$. The parameter $\xi_p^*$ is determined for various hadrons at various centre of mass energies. The dependence on the hadron type poses some interesting questions about the process of hadron-formation. The dependence of $\xi^*_p$ on the centre of mass energy is seen to be described adequately by perturbation theory. A quantitative check of LPHD + MLLA is possible by extracting a value of $\alpha_s$ from an overall fit to the scaling behaviour of $\xi^*_p$.