Pion and $\rho$ meson's unpolarized quark distribution functions from $q\bar{q}$ and all Fock-states within Dyson--Schwinger equations

TL;DR

This paper calculates the unpolarized quark distribution functions of the pion and rho meson using Dyson-Schwinger equations, revealing the importance of higher Fock states and helicity-dependent differences.

Contribution

It introduces a new DSE framework for spin-1 hadrons and computes the rho meson's PDFs for different helicity states, including tensor-polarized distributions, highlighting higher Fock-state effects.

Findings

First-time calculation of rho meson PDFs for different helicity states.

Significant differences between helicity states in rho meson PDFs.

Higher Fock states significantly affect quark distribution functions.

Abstract

We compute the twist-2 unpolarized quark parton distribution functions (PDFs) of the pion and the $\rho$ meson within the Dyson-Schwinger equations (DSEs) framework using the rainbow-ladder (RL) truncation. A new DSE for the spin-1 hadron's quark-quark correlation matrix is derived, from which the PDFs can be extracted. For the $\rho$ meson, we obtain for the first time within RL-DSEs the unpolarized PDFs corresponding to different helicity states. A pronounced difference is observed between the $|\Lambda|=1$ and $\Lambda=0$ cases, where $\Lambda$ denotes the meson helicity, leading to a nonvanishing and numerically sizable tensor-polarized PDF $f_{1LL}(x)$. We further compare these results with those obtained under a leading Fock-state ($|q\bar{q}\rangle$) truncation and find substantial deviations. This comparison demonstrates that the present RL-DSEs framework incorporates higher Fock-state contributions associated with gluonic degrees of freedom, which has a significant impact on the quark distributions.