Results

The corrected scaled momentum distributions (with statistical errors only) are shown in figure 1, overlaid with the distributions from the ARIADNE Monte Carlo [8]. The Monte Carlo reproduces the data well in all bins of x, Q² and x_p.

In the region of low x and Q² the distributions peak at x_p $\approx$ 0.15; as Q² increases this peak disappears and the data fall off sharply from x_p = 0.02. Scaling violations can be seen, as predicted, in the gradual steepening of the gradients of the distributions as Q² increases. To show this more clearly, in figure 2 the data are plotted in fixed bins of x_p as a function of Q². Scaling violations appear at high Q² and high x_p as a negative slope with increasing Q². The turnover observed in the ZEUS data at low x_p and low Q² can be attributed to depopulation of the current region by processes not present in e⁺e^- interactions (e.g. boson-gluon fusion). The ZEUS data are compared with data from e⁺e^- experiments (divided by a factor 2) and with a next-to-leading-order calculation, CYCLOPS [9]. The e⁺e^- data points are taken from the aforementioned LEP study of scaling violations in fragmentation functions and have been corrected for the decays of K⁰_S and $\Lambda$. There is good agreement with the ZEUS data. The NLO calculation combines a full next-to-leading order matrix element with the MRSA' parton densities [10] and NLO fragmentation functions derived by Binnewies et al. from fits to e⁺e^- data [11]. There is good agreement with the ZEUS data for Q² $\geq$ 80 GeV²; below this value there are large theoretical uncertainties.