Model Calculation of Pion Parton Distribution Functions in the Valence Region

We calculate parton distribution functions of the pion, for the range of 0.1≤x≤0.60, based on the soft dynamics of the partons

within the valence-cluster-residual field model. Within this model we assume that the soft partonic structure of the pion is defined by the quark anti-quark valence cluster embedded in the residual field of the pion. The parton distribution function is calculated using phenomenological

wave functions for the quark anti-quark valence​ cluster and the residual field. Our result indicate that the peak position of x weighted valence parton distribution

depends on the mass of the residual system and the parameters of the system are obtained by fitting the height and the peak position

of this distribution to extracted PDFs. This comparison reveals that unlike for the case of nucleon PDF, very little residual mass

is needed to describe existing pion PDFs at intermediate x. Additionally with the obtained parameters we describe reasonably well

the high x distribution of the pion which is in agreement with recent estimations.