Pion Valence Structure at Intermediate x in the Residual Field Approach

Abstract

We calculate the valence parton distribution function~(PDF) of pion, within the theoretical approach based on spectral function representation of valence quarks in the pion. In this approach we assume that the soft partonic structure of pion is defined by the valence $q\bar q$ cluster, consisting of current quarks, embedded in the residual field of the pion. The valence 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 cluster and the mass of the residual system. Magnitudes of these parameters are obtained by fitting to the height and the peak position of empirical pion xPDF evaluated at starting $Q_0$. They indicate that unlike the nucleon case, very little residual mass is needed to describe existing pion PDFs at intermediate x. They also indicate that the $q\bar q$-cluster is highly virtual and on average the interacting quark carries 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, and practically describing $\sim (1-x)$ 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.

Figures (3)

• Figure 1: Feynman Diagrams for Deep Inelastic Scattering in Residual-Mean Field model. (a) General case for hadrons with $qqq$ or $q\bar{q}$ clusters. (b) For the case of deep inelastic scattering from pion.
• Figure 2: Description of x-weighted pion PDF at $Q_0=1.3$ GeV for $m_R=0$, $m_V=0.95$ GeV and $B_R = 1.2$ GeV$^{-2}$.
• Figure 3: The $x_R$ dependence of response function $R(x_R)$ at different $Q^2$.