Study of $e^{+}{e}^{-}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\yen (1D)$ at Belle II

Abstract

The bottomonium spectrum, consisting of bound states of a $b$ quark and an anti-$b$ quark, provides an excellent laboratory for probing quantum chromodynamics in the non-perturbative regime. While $S$ and $P$-wave bottomonium states are well studied experimentally, information on $D$-wave states remains scarce. We search for $D$-wave bottomonium state via the decay of a vector bottomonium-like state $\hat{I}\yen (10753)$ in the reaction $e^{+}{e}^{-}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\yen (1D)$, using $19.6{\mathrm{fb}}^{-1}$ of data collected with the Belle II detector at center-of-mass energies $\sqrt{s}=10.653,10.701,10.745$, and $10.805$~GeV, in the vicinity of the $\hat{I}\yen (10753)$ resonance. No significant signals are observed. Upper limits at the 90% credibility level are set on the products of the cross sections and branching fractions, $\ddot{I}ƒ[e^{+}{e}^{-}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{\yen }_2(1D)]\times \mathcal{B}[\hat{I}{\yen }_2(1D)\to {\hat{I}}^3\ddot{I}{‡}_{b1}]$ and $\ddot{I}ƒ[e^{+}{e}^{-}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{\yen }_3(1D)]\times \mathcal{B}[\hat{I}{\yen }_3(1D)\to {\hat{I}}^3\ddot{I}{‡}_{b2}]$, at each center-of-mass energy.

22 pages, 4 figures