An Analysis of Momentum Fractions of Quarks and Gluons in a model of Proton

TL;DR

This paper estimates the bounds of quark and gluon momentum fractions in a proton model using the momentum sum rule, within a specific x-range, aligning with QCD expectations.

Contribution

It introduces a self-similarity based model to compute momentum fraction bounds in a limited x-range, extending understanding of proton structure.

Findings

Bounds conform to asymptotic QCD expectations

Model valid in x-range 6.2×10⁻⁷ to 10⁻²

Provides estimates for quark and gluon momentum fractions

Abstract

Momentum sum rule can be used as an inequality to estimate the lower and upper bounds of the momentum fractions of quarks and gluons in a model of proton valid in a limited \textit{x} range. We compute such bounds in a self-similarity based model of proton structure function valid in the range $ 6.2\times 10^{-7} \leq x \leq 10^{-2} $. The results conform to the asymptotic QCD expectations.