Possible Universal Limit for Valence Parton Distributions

Abstract

We report the observation of the existence of a possible universal limit for valence parton distributions that should exist once partonic degrees of freedom are relevant for high energy scattering from strongly interacting bound systems like a nucleon, meson or a few nucleon system at very short distances. Our observation is based on the notion that the Bjorken x weighted valence parton distribution function has a peak, $x_p$, that characterizes the average momentum fraction carried out by the valence quarks in the system. Within the residual mean-field model of the valence quark distribution we found that $x_p$ has an upper limit: $x_p\le \frac{1}{2(n_V-1)}$, where $n_V$ is the number of valence quarks which can be considered in the cluster embedded in the strongly interacting environment of the bound system. The existence of such a limit imposes a new constraint on choosing the starting resolution scale $Q_0$ for PDFs. Our prediction for the nucleon is that $x_p{\mid }_{Q\to Q_0}\le \frac{1}{4}$, which is in agreement with all the available valence PDFs that employ the standard approach for selecting starting $Q_0$. We also demonstrate how the existence of this limit can be used to check the onset of quark-clusters in short range nucleon correlations in nuclei.

Comments: Main article 9 pages with 5 figures