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

We investigate the partonic structure of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>ρ</a:mi> </a:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>ρ</c:mi> </c:math> 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.