Pion Valence Quark Distributions from Maximum Entropy Method

TL;DR

This paper uses a maximum entropy approach to deduce pion valence quark distributions at low resolution scales and evolves them to higher scales, achieving consistency with experimental data and providing insights into nonperturbative QCD structure.

Contribution

It introduces a maximum entropy method to determine pion valence quark distributions at very low Q^2, incorporating evolution to match experimental results.

Findings

Valence quark distributions at low Q^2 are deduced successfully.

Evolved distributions agree with Drell-Yan experimental data.

First three moments of distributions are consistent with other models.

Abstract

Valence quark distributions of pion at very low resolution scale $Q^{2}_0 \sim 0.1~GeV^2$ are deduced from a maximum entropy method, under the assumption that pion consists of only a valence quark and a valence anti-quark at such a low scale. Taking the obtained initial quark distributions as the nonperturbative input in the modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (with the GLR-MQ-ZRS corrections) evolution, the generated valence quark distribution functions at high $Q^2$ are consistent with the measured ones from a Drell-Yan experiment. The maximum entropy method is also applied to estimate the valence quark distributions at relatively higher $Q^2$ = 0.26 GeV$^{2}$. At this higher scale, other components (sea quarks and gluons) should be considered in order to match the experimental data. The first three moments of pion quark distributions at high $Q^2$ are calculated and compared with the other theoretical predictions.