Exploring $T_{\Upsilon\Upsilon}$ tetraquark candidates in a coupled-channels formalism

Abstract

We investigate the spectrum of $T_{\Upsilon\Upsilon}$ tetraquark candidates within a coupled-channels framework. The analysis includes all $L\leq2$ combinations of $\Upsilon(1S)$, $\Upsilon(2S)$, $\eta_b(1S)$, and $\eta_b(2S)$ in the $J^P = 0^\pm, 1^\pm, 2^\pm$ sectors. The meson-meson interaction is derived from an underlying constituent quark model through the resonating group method, and the properties of the states are obtained from poles of the scattering matrix. We find a rich spectrum of resonant, and virtual, states distributed between the $\eta_b(1S)\eta_b(1S)$ and $\Upsilon(2S)\Upsilon(2S)$ thresholds. The pattern of poles exhibits approximate heavy-quark spin symmetry multiplets. Several states are dominated by a single channel and can be associated with threshold-driven structures, while higher-mass resonances show sizable mixing among channels involving radially excited bottomonia. The predicted widths range from tens to several hundred MeV. Branching ratios indicate that many states couple predominantly to final states with at least one excited bottomonium, whereas only a subset of the spectrum is expected to be visible in the $\eta_b(1S)\eta_b(1S)$, $\eta_b(1S)\Upsilon(1S)$ and $\Upsilon(1S)\Upsilon(1S)$ channels. These results provide quantitative guidance for experimental searches of fully heavy tetraquarks and offer a test of coupled-channel dynamics and heavy-quark spin symmetry in the $bb\bar b\bar b$ sector.