Abstract
Recently, Belle Collaboration has reported the measurement of the spin-flipping transition $\Upsilon(4S) \to h_b(1P)\eta$ with an unexpectedly large branching ratio: $\mathcal{B}(\Upsilon(4S) \to h_b(1P)\eta) =(2.18\pm 0.11\pm 0.18)\times 10^{-3}$. Such a large branching fraction contradicts with the anticipated suppression for the spin flip. In this work, we examine the effects induced by intermediate bottomed meson loops and point out that these effects are significantly important. Using the effective Lagrangian approach (ELA), we find the experimental data on $\Upsilon(4S) \to h_b(1P)\eta$ can be accommodated with the reasonable inputs. We then explore the decays $\Upsilon(5S,6S)\to h_b(1P)\eta$ and find that these two channels also have sizable branching fractions. We also calculate these these processes in the framework of nonrelativistic effective field theory (NREFT). For the decays $\Upsilon(4S) \to h_b(1P) \eta$, the NREFT results are at the same order of magnitude but smaller than the ELA results by a factor of $2$ to $5$. For the decays $\Upsilon(5S, 6S) \to h_b(1P) \eta$ the NREFT results are smaller than the ELA results by approximately one order of magnitude. We suggest future experiment Belle-II to search for the $\Upsilon(5S, 6S)\to h_b(1P) \eta$ decays which will be helpful to understand the transition mechanism.
Highlights
In recent years, bottomonium transitions with an η meson or two pions in the final state have been extensively studied on the experimental side [1,2,3,4,5,6,7]
A nonrelativistic effective field theory (NREFT) is used in Ref. [11], where the branching ratio can reach the order of 10−3. It has been noticed for a long time that the intermediate meson loop (IML) is one prominent nonperturbative mechanism in hadronic transitions [12,13,14]
Recent experiments on the Υð4SÞ → hbð1PÞη transition show anomalously large decay rates. This seems to contradict the naive expectation that hadronic transitions with spin flipping terms should be suppressed with respect those that do not have these terms
Summary
Bottomonium transitions with an η meson or two pions in the final state have been extensively studied on the experimental side [1,2,3,4,5,6,7]. It has been noticed for a long time that the intermediate meson loop (IML) is one prominent nonperturbative mechanism in hadronic transitions [12,13,14] In recent years, this mechanism has been successfully applied to study the production and decays of ordinary and exotic states [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45], and a global agreement with experimental data is found.
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