Gluon TMDs for tensor polarized deuteron in a spectator model

Abstract

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.

Figures (5)

• Figure 1: Upper-left panel: Fit of the integrated unpolarized gluon TMD $xf_1(x)$ for the deuteron at $Q_0 = 2\,\mathrm{GeV}$ in the range $0.001 < x < 1$. The band with dashed borders corresponds to the nNNPDF1.0 parametrization of $xf_1$AbdulKhalek:2019mzd. The solid line shows the result for replica 60. The cyan band represents the 68% uncertainty band of the spectator model fit. The other three panels display the $x$-dependence of $xh_1^{\perp(1)}$, $xg_1$, and $xg_{1T}^{(1)}$ obtained from the spectator model using the parameters in Table \ref{['table:parm']}.
• Figure 2: The integrated LL tensor-polarized TMDs as functions of $x$ at $Q_0 = 2\,\mathrm{GeV}$. The band represents the 68% uncertainty of the TMDs, and the solid line corresponds to replica 60.
• Figure 3: The integrated LT and TT tensor-polarized TMDs as functions of $x$ at $Q_0 = 2\,\mathrm{GeV}$. Conventions as in Fig. \ref{['fig:x2']}. Left column: LT-polarized PDFs $xf_{1LT}^{(1)}$, $xh_{1LT}^{(1)}$, and $xh_{1LT}^{\perp(2)}$. Right column: TT-polarized PDFs $xf_{1TT}^{(1)} - xh_{1TT}^{\perp(1)}$, $xh_{1TT}$, and $xh_{1TT}^{\perp\perp(2)}$.
• Figure 4: The unpolarized, vector-polarized, and LL tensor-polarized TMDs (replica 60) as functions of $\bm{k}_T^2$ for $x = 0.001$, $0.01$, and $0.1$ at $Q_0 = 2\,\mathrm{GeV}$. Solid line: $x = 0.001$; dashed line: $x = 0.01$; dotted line: $x = 0.1$.
• Figure 5: The LT and TT tensor-polarized TMDs (replica 60) as functions of $\bm{k}_T^2$ for $x = 0.001$, $0.01$, and $0.1$ at $Q_0 = 2\,\mathrm{GeV}$. Line conventions as in Fig. \ref{['fig:kt1']}.