Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge I.} Bottomonia

Abstract

In the framework of the spectral integral equation, we consider the $b\bar{b}$ states and their radiative transitions. We reconstruct the $b\bar{b}$ interaction on the basis of data for the levels of the bottomonium states with $J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, $1^{++}$, $2^{++}$ as well as the data for the radiative transitions ${\rm Y}(3S)\to \gamma {\chi }_{bJ}(2P)$ and ${\rm Y}(2S)\to \gamma {\chi }_{bJ}(1P)$ with $J=0,1,2$. We calculate bottomonium levels with the radial quantum numbers $n\le 6$, their wave functions and corresponding radiative transitions. The ratios $Br[{\chi }_{bJ}(2P)\to \gamma {\rm Y}(2S)]/Br[{\chi }_{bJ}(2P)\to \gamma {\rm Y}(1S)]$ for $J=0,1,2$ are found in the agreement with data. We determine the $b\bar{b}$ component of the photon wave function using the data for the $e^{+}{e}^{-}$ annihilation, $e^{+}{e}^{-}\to {\rm Y}(9460)$, ${\rm Y}(10023)$, ${\rm Y}(10036)$, ${\rm Y}(10580)$, ${\rm Y}(10865)$, ${\rm Y}(11019)$, and predict partial widths of the two-photon decays ${\eta }_{b0}\to \text{ggam}$, ${\chi }_{b0}\to \text{ggam}$, ${\chi }_{b2}\to \text{ggam}$ for the radial excitation states below $B\bar{B}$ threshold ($n\le 3$).

Comments: 43 pages, 13 figures