Possibility to observe highern3D1bottomonium states in thee+e−processes

Abstract

The possibility to observe new bottomonium states with ${J}^{PC}={1}^{--}$ in the region 10.7--11.1 GeV is discussed. The analysis of the dielectron widths shows that the $(n+1)^{3}S_{1}$ and $n^{3}D_{1}$ states ($n\ensuremath{\ge}3$) may be mixed with a rather large mixing angle, $\ensuremath{\theta}\ensuremath{\approx}30\ifmmode^\circ\else\textdegree\fi{}$, and this effect provides the correct values of ${\ensuremath{\Gamma}}_{ee}(\ensuremath{\Upsilon}(10580))$ and ${\ensuremath{\Gamma}}_{ee}(\ensuremath{\Upsilon}(11020))$. On the other hand, the $S\ensuremath{-}D$ mixing gives rise to an increase by 2 orders of magnitude of the dielectron widths of the mixed $\stackrel{\texttildelow{}}{\ensuremath{\Upsilon}}(n^{3}D_{1})$ resonances ($n=3$, 4, 5), which originate from pure $D$-wave states. The value ${\ensuremath{\Gamma}}_{ee}(\stackrel{\texttildelow{}}{\ensuremath{\Upsilon}}(3D))={0.095}_{\ensuremath{-}0.025}^{+0.028}\text{ }\text{ }\mathrm{keV}$ is obtained, being only $\ensuremath{\sim}3$ times smaller than the dielectron width of $\ensuremath{\Upsilon}(10580)$, while ${\ensuremath{\Gamma}}_{ee}(\stackrel{\texttildelow{}}{\ensuremath{\Upsilon}}(5D))\ensuremath{\sim}135\text{ }\text{ }\mathrm{eV}$ appears to be close to ${\ensuremath{\Gamma}}_{ee}(\ensuremath{\Upsilon}(11020))$ and therefore this resonance may become manifest in the ${e}^{+}{e}^{\ensuremath{-}}$ experiments. The mass differences between $M(nD)$ and $M((n+1)S)$ ($n=4$, 5) are shown to be rather small, $50\ifmmode\pm\else\textpm\fi{}10\text{ }\text{ }\mathrm{MeV}$.