The Pion Parton Distribution Puzzle in the High x Region

We developed a new theoretical approach in the description of partonic structure of hadrons based on spectral function representation of valence quarks. In this approach massless valence quarks are considered in the mean field of residual hadron. This approach initially was applied to the calculation of parton distribution function~(PDF) of nucleons that resulted in an observation of pion-cloud structure of nucleon. In this report we present our calculation of pion PDF in the valence region within the same approach. In this approach we describe the soft partonic structure of pion through the valence $q\bar q$ cluster, embedded in the residual field of the pion. The pion PDF is calculated using phenomenological Light-Front wave functions for the $q\bar q$ cluster and the residual field. Our result indicates that the peak position of the x weighted valence PDF~(xPDF) depends on parameters characterizing the virtuality of the $q\bar q$ cluster and the mass of the residual system. These parameters are evaluated by fitting the calculated PDF to the height and the peak position of empirical pion xPDF at starting $Q_0$. They indicate that unlike the nucleon case, very little residual mass is needed in the pion to describe existing pion PDFs in the valence region. They also require the $q\bar q$-cluster to be highly virtual with the interacting quark carrying almost all of the momentum of the $q\bar q$ cluster. This picture is consistent with the dominance of the Feynman mechanism leaving little room for the hard component in the PDF. The calculation practically describes the $\sim (1-x)$ behavior observed recently at $x\to 1$ limit. Our non-trivial observation is that the height and the peak position of xPDF define the analytic behavior of valence PDF at $x\to 1$ limit.