LAUSR

We present a covariant formulation and model calculations of the leading-twist time-reversal even transverse-momentum-dependent quark distribution functions (TMDs) for a spin-one target. Emphasis is placed on a description of these three-dimensional distribution functions which is independent of any constraints on the spin quantization axis. We apply our covariant spin description to all nine leading-twist time-reversal even $\ensuremath{\rho}$ meson TMDs in the framework provided by the Nambu--Jona-Lasinio model, incorporating important aspects of quark confinement via the infrared cutoff in the proper-time regularization scheme. In particular, the behaviors of the three-dimensional TMDs in a tensor polarized spin-one hadron are illustrated. Sum rules and positivity constraints are discussed in detail. Our results do not exhibit the familiar Gaussian behavior in the transverse momentum, and other results of interest include the finding that the tensor polarized TMDs---associated with spin-one hadrons---are very sensitive to quark orbital angular momentum, and that the TMDs associated with the quark operator ${\ensuremath{\gamma}}^{+}{\mathbf{\ensuremath{\gamma}}}_{T}{\ensuremath{\gamma}}_{5}$ would vanish were it not for dynamical chiral symmetry breaking. In addition, we find that 44% of the $\ensuremath{\rho}$ meson's spin is carried by the orbital angular momentum of the quarks, and that the magnitude of the tensor polarized quark distribution function is about 30% of the unpolarized quark distribution. A qualitative comparison between our results for the tensor structure of a quark-antiquark bound state is made to existing experimental and theoretical results for the two-nucleon (deuteron) bound state.