$X(3872)$, $X_b$, and the ${\chi }_{b1}(3P)$ state

Abstract

We discuss the possible production and discovery channels in $e^{+}{e}^{-}$ and $pp$ machines of the $X_b$, the bottomonium counterpart of $X(3872)$ and the putative isoscalar analogue of the charged bottomonium-like states $Z_b$ discovered by Belle. We suggest that the $X_b$ may be close in mass to the bottomonium state ${\chi }_{b1}(3P)$, mixing with it and sharing its decay channels, just as $X(3872)$ is likely a mixture of a $\bar{D}{D}^{\ast }$ molecule and ${\chi }_{c1}(2P)$. Consequently, the experiments which reported observing ${\chi }_{b1}(3P)$ might have actually discovered the $X_b$, or a mixture of the two states.

Comments: 10 pages, no figures, to be published in Phys. Rev. D. References and text added; misprints corrected