Experimental momentum spectra of identified hadrons in jets and the   predictions from LPHD + MLLA
  Experimental data on the shape of hadronic momentum spectra are compared with 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. It is interesting to look at the dependence of $\xi^*_p$ on the hadron type. This is used to study the influence of the hadron type on the cut-off scale $Q_0$ in the parton shower development. The dependence of $\xi^*_p$ on the centre of mass energy is seen to be described adequately by perturbation theory. The approach is made quantitative by extracting a value of $\alpha_s(m_Z)$ from an overall fit to the scaling behaviour of $\xi^*_p$. 
Nichol. C. Brummer