Valence quark distribution of rho meson using light-front quark model

TL;DR

This paper studies the internal quark structure of the rho meson using a light-front quark model, deriving PDFs and TMDs, and emphasizing the importance of tensor polarization in its 3D structure.

Contribution

It introduces a detailed calculation of rho meson PDFs and TMDs within the light-front quark model, including tensor polarization effects and NLO evolution.

Findings

Tensor polarization significantly influences the rho meson's 3D structure.

Evolved PDFs agree with existing theoretical predictions.

Positivity constraints are satisfied in the model.

Abstract

We investigate the partonic structure of the $\rho$ meson, the lightest spin-$1$ vector meson, within the light-front quark model (LFQM). To explore the sensitivity to model assumptions, we employ two distinct types of spin wave functions in the LFQM. Using light-front helicity wave functions, we derive explicit expressions for the leading-twist and subleading-twist quark parton distribution functions (PDFs), and evolve the leading-twist PDFs to higher scales with next-to-leading order (NLO) Dokshitzer--Gribov--Lipatov--Altarelli--Parisi (DGLAP) evolution. We have also calculated the Mellin moment from the evolved PDFs using a simple neural network frame and compared with available theoretical predictions. Furthermore, we compute the full set of nine leading-twist transverse-momentum-dependent distributions (TMDs) for the valence quark in the $\rho$ meson, including three tensor TMDs that arise from spin-$1$ tensor polarization of the hadron. Positivity constraints for the PDFs and TMDs are examined within this framework. Our findings highlight the crucial role of tensor polarization in shaping the three-dimensional partonic structure of vector mesons.