Decays of $Υ(10860)$ and $Υ(10753)$ into $ωχ_{bJ}$

TL;DR

This work addresses bottomonium states above open-bottom threshold by modeling Υ(10580) and Υ(10753) as a $4S$-$3D$ mixture and Υ(10860) as a $5S$-$4D$ mixture, predicting a yet-unobserved Υ(10950) as the mixing partner of Υ(10860). Using a nonrelativistic effective field theory with heavy quark spin symmetry, the authors separate short-range tree-level decays from open-bottom meson loop effects, especially for the D-wave component, and fix mixing angles from dielectron widths Γ_{ee} and masses. The analysis reconciles Belle and Belle II data on ωχ_{bJ} decays, yields specific θ and θ' values, and provides predictions for Γ_{ee} and partial widths Γ(Υ→χ_{bJ}ω) for Υ(10753) and Υ(10950). The predicted Υ(10950) has a small Γ_{ee} that explains its non-observation in e^{+}e^{-} collisions, while its ωχ_{bJ} decay widths offer experimental probes of the mixing framework and open-bottom dynamics.

Abstract

In this paper, we model $Υ(10753)$ as a $4S$-$3D$ bottomonium mixture and $Υ(10860)$ as a $5S$-$4D$ mixture, and predict the properties of a new bottomonium state, $Υ(10950)$, as the mixing partner of $Υ(10860)$. The mixing angles are derived from dielectron decay widths and mass shifts of these bottomonia. We consider open-bottom meson loops in the decays of the $D$-wave bottomonium components, based on a nonrelativistic effective field theory power counting. We show that the $S$-$D$ mixing scheme is consistent with the experimental data of the decays of $Υ(10860)$ into $ωχ_{bJ}$ ($J=0,1,2$) and $Υ(10753)$ into $ωχ_{bJ}$ ($J=1,2$). Predictions for the dielectron widths and partial decay widths into $χ_{bJ}ω$ for $Υ(10753)$ and $Υ(10950)$ are presented.

Figures (6)

• Figure 1: Short-range contribution for the transitions $\Upsilon_{S,\,D}\to \omega \chi_{bJ}$.
• Figure 2: Dominant coupled-channel effects for $\Upsilon_D$ decaying into $\omega \chi_{bJ}$. The dashed lines represent two unitary cuts. The charge conjugated diagram is not shown.
• Figure 3: Dependence of the ratios $R_{02}$ and $R_{12}$ on the $\Upsilon$ mass: (a) for $S$-wave bottomonium decay, (b) for $D$-wave bottomonium decay. The vertical dot-dashed lines indicate the thresholds of $B_1 \bar{B}$, $B_1\bar{B}^*$ and $B_2^*\bar{B}^*$. In (b), the solid and dotted curves represent the results with and without considering the finite widths of $B_1$ and $B_2^*$, respectively.
• Figure 4: Dependence of ratio $R_{01}$ on ratio $R_{12}$ for the $4S$-$3D$ mixing of $\Upsilon(10753)$.
• Figure 5: Dependence of the masses of $5S$-$4D$ mixed states on the mixing angle $\theta'$. The pink band represents the measured mass of $\Upsilon(10860)$, and the purple band shows the predicted mass of $\Upsilon'(4D)$. The pure $5S$ and $4D$ state masses are taken to be 10894 MeV and 10942 MeV, respectively, based on the quark model with a flattened potential in the non-relativistic limit Badalian:2009bu.