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

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 $\ensuremath{\rho}$, $J/\ensuremath{\psi}$ and $\mathrm{\ensuremath{\Upsilon}}$. We employ the leading Fock-state light front wave functions (LF-LFWFs) of $\ensuremath{\rho}$ and $J/\ensuremath{\psi}$ from our recent study, and supplement with $\mathrm{\ensuremath{\Upsilon}}$'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 nonvanishing and evolve with current quark mass, in particular the tensor polarized TMDs ${f}_{1LT}$ and ${f}_{1TT}$ which undergo a sign flip. The $\ensuremath{\rho}$ 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 $\ensuremath{\rho}$'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 the lattice QCD prediction. The qualitative behavior of tensor polarized PDF ${f}_{1LL}(x)$ in $\ensuremath{\rho}$ at large $x$ is also discussed.