The Evolution of Hadron Spectra in the Modified Leading Logarithm Approximation

We perform fits of $\Lambda_{\rm QCD}$ and the gluon fragmentation function $D(x,Q)$ at initial scale $Q_0 \gg\Lambda_{\rm QCD}$ to charged light hadron momentum spectra data by evolving in the Modified Leading Logarithm Approximation. Without additional assumptions, we achieve a good description of the available data for $\xi=\ln(1/x)$ up to and around the Gaussian peak, and values of $\Lambda_{\rm QCD}$ acceptably close to those in the literature. In particular, we find that this procedure describes the position of the peak, and, in contrast to the Limiting Spectrum, also the normalization.