The recent observation and measurement of the decay $Z_c(3900)\to \rho {\eta }_c$ provides the data on the relative strength of the pion and $\rho$ coupling in the corresponding transitions between exotic resonances and pure heavy quarkonium. It is argued that using these data, the heavy quark limit for the $c$ and $b$ quarks, the heavy quark spin symmetry (HQSS) and the vector dominance for photon emission by the light quarks, one can (approximately) quantitatively estimate the rates of the radiative transitions from $\mathrm{\Upsilon }(5S)$ to the expected $G$-odd states of molecular bottomonium $W_{bJ}$. The estimate of the cross section of the processes $e^{+}{e}^{-}\to \gamma W_{bJ}$ at the maximum of the $\mathrm{\Upsilon }(5S)$ resonance comes out in the ballpark of 0.1 pb, which sets a benchmark for a possible search for these processes at BelleII.

• Received 20 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.034025

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Published by the American Physical Society