Abstract
We perform the investigation of two-body hidden-bottom transitions of the $\Upsilon(6S)$, which include $\Upsilon(6S) \to \Upsilon(1^3D_J) \eta~~(J=1,2,3)$ decays. For estimating the branching ratios of these processes, we consider contributions from the triangle hadronic loops composed of S-wave $B_{(s)}$ and $B_{(s)}^*$ mesons, which are a bridge to connect the $\Upsilon(6S)$ and final states. Our results show that both of the branching ratios of these decays can reach $10^{-3}$. Due to such considerable potential to observe these two-body hidden-bottom transitions of the $\Upsilon(6S)$, we suggest the forthcoming Belle II experiment to explore them.
Highlights
As an updated accelerator with luminosity 8 × 1035 cm−2 s−1, SuperKEKB is currently being constructed
The αΛ dependence of the branching ratios for the processes Υ ð6SÞ → Υð13DJÞηðJ 1⁄4 1; 2; 3Þ. These significant values of the branching ratios show that the Υð6SÞ → Υð13DJÞη decays can be accessible at Belle II
Theorists have made great efforts to explore the underlying mechanisms [4,5,6,7,8,9,10,13,15], and have revealed that the hadronic loop mechanism, which is an equivalent description of the coupled-channel effect, plays an important role for understanding these anomalous transitions of Υð5SÞ
Summary
As an updated accelerator with luminosity 8 × 1035 cm−2 s−1, SuperKEKB is currently being constructed. In this work, using the hadronic loop mechanism, we calculate the branching ratios of the discussed Υ ð6SÞ → Υð13DJÞη decays, by which the potential observation of. These two-body hidden-bottom transitions at Belle II can be suggested. The monopole form factor F ðq2Þ 1⁄4 ðm2E − Λ2Þ=ðq2 − Λ2Þ is introduced in our calculation since the structure effect of the interaction vertex cannot be ignored and off-shell effect from the exchanged bottom mesons in triangle loops should be compensated by this way This type of form factor is supported by the QCD sum rule study [26]. 11 3 8π jp⃗ ηj m2Υ ð6SÞ jMTJ otal j2 ; ð25Þ which averages over the polarization of initial Υð6SÞ and sums over the polarizations of the Υð13DJÞ
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