Transverse momentum distributions of valence quark in light and heavy vector mesons

TL;DR

This paper investigates the transverse momentum dependent parton distribution functions of light and heavy vector mesons using light front wave functions, revealing their evolution, sign changes, and comparison with other models and lattice QCD.

Contribution

It provides a comprehensive study of vector meson TMDs and PDFs using light front overlap representation and Bethe-Salpeter wave functions, including heavy mesons like $J/ ho$ and $$Upsilon.

Findings

All TMDs are non-vanishing and evolve with quark mass.

Tensor polarized TMDs $f_{1LT}$ and $f_{1TT}$ undergo a sign flip.

Valence PDFs agree with lattice QCD predictions at 2.4 GeV.

Abstract

We study the leading-twist time-reversal even transverse momentum dependent parton distribution functions (TMDs) of light and heavy vector mesons, i.e., the $\rho$, $J/\psi$ and $\Upsilon$. We employ the leading Fock-state light front wave functions (LF-LFWFs) of $\rho$ and $J/\psi$ from our recent study, and supplement with $\Upsilon$'s LF-LFWFs. These LF-LFWFs are extracted from dynamically solved Bethe-Salpeter wave functions. The vector meson TMDs are then studied with the light front overlap representation at leading Fock-state. All the obtained TMDs are non-vanishing and evolve with current quark mass, in particular the tensor polarized TMDs $f_{1LT}$ and $f_{1TT}$ which undergo a sign flip. The $\rho$ TMDs are compared with other model studies and agreement is found, aside from $f_{1LT}$ and $f_{1TT}$. Finally, the collinear PDFs of vector mesons are studied. The $\rho$'s valence PDFs $f_{1,v}(x)$ and $g_{1L,v}(x)$ are evolved to the scale of 2.4 GeV, with their first three moments compared to lattice QCD prediction. The qualitative behavior of tensor polarized PDF $f_{1LL}(x)$ in $\rho$ at large $x$ is also discussed.