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

Anisovich, V. V.; Dakhno, L. G.; Matveev, M. A.; Nikonov, V. A.; Sarantsev, A. V.

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

Authors

Description

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 $Υ(3S) \toγχ_{bJ}(2P) $ and $Υ(2S) \toγχ_{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 $Br[χ_{bJ}(2P)\toγΥ(2S)]/Br[χ_{bJ}(2P)\toγΥ(1S)]$ 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, $e^+e^- \toΥ(9460)$, $Υ(10023)$, $Υ(10036)$, $Υ(10580)$, $ Υ(10865)$, $Υ(11019)$, and predict partial widths of the two-photon decays $η_{b0}\to\ggam$, $χ_{b0}\to\ggam$, $χ_{b2}\to\ggam$ for the radial excitation states below $B\bar B$ threshold ($n\le 3$).
43 pages, 13 figures