Possible Universal Limit for Valence Parton Distributions

TL;DR

This paper proposes a universal upper limit for the peak of valence parton distributions in hadrons, based on a residual mean-field model, which constrains the initial scale for PDFs and relates to short-range nucleon correlations.

Contribution

It introduces a new theoretical limit on valence quark momentum fractions, linking the peak position to the number of valence quarks and providing a constraint on the initial PDF scale.

Findings

Predicted upper limit for the valence distribution peak in nucleons is 1/4.

The limit is consistent with existing valence PDFs.

The approach offers a way to identify quark-cluster onset in nuclei.

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: $x_p \leq {1\over 2(n_V-1)}$, 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 $x_p\mid_{Q\to Q_0}\le{1\over 4}$, 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.