Gluon TMDs for tensor polarized deuteron in a spectator model

We present a model calculation of the transverse-momentum-dependent distributions (TMDs) for gluons in a tensor-polarized deuteron. Our model is based on the assumption that an on-shell deuteron can emit a time-like off-shell gluon, while the remaining system is treated as a single on-shell spectator particle whose mass can take on a continuous range of real values, described by a spectral function. For spin-1 hadrons, the polarization is characterized not only by a spin vector $S$ but also by a symmetric traceless spin tensor $T$. The deuteron-gluon-spectator coupling is described by an effective vertex containing three form factors. We obtain analytical expressions for thirteen T-even gluon TMDs. We also provide numerical results for the $x$-dependence and $\bm{k}_T$-dependence of these TMDs. Our analysis reveals non-negligible results of these gluon TMDs, especially for tensor-polarized hadrons, which could potentially be explored in future experimental measurements.