Review of bottomonium studies at Belle

B-factories, the BaBar and Belle experiments, produced many highlights in the bottomonium physics. Among them are: • observation of the spin-singlet states ηb(1S ), ηb(2S ), hb(1P) and hb(2P); • observation of charged bottomonium-like states Zb(10610) and Zb(10650) with exotic quark content; • observation of anomalous transitions from the Υ(4S ), Υ(10860) and Υ(11020). Here we present three recent results from Belle: the new measurement of the ηb(1S ) mass [1], the observation of the Υ(4S ) → Υ(1S )η′ transition [2], and the observation of the e+e− → χbJ(1P)πππ process in the Υ(11020) region [3].


New measurement of the η b (1S ) mass
There is a substantial disagreement between various measurements of the η b (1S ) mass [4]. Those from the Υ(2S , 3S ) → η b (1S )γ transitions measured by BaBar and CLEO are grouped near 9390 MeV/c 2 , while those from the h b (1P, 2P) → η b (1S )γ transitions measured by Belle are clustered near 9400 MeV/c 2 . To improve on this, Belle studied the Υ(2S ) → η b (1S )γ transition using the 24.7 fb −1 Υ(2S ) data sample. Like previous measurements, Belle used inclusive reconstruction: the energy spectrum of all photons was investigated. Selection requirements include suppression of the light quark production using event topology and π 0 veto. The γ spectrum after subtraction of the smooth component of the fit function is shown in figure 1. The significance of the η b (1S ) signal exceeds 7 standard deviations (σ), and this is the first observation of the Υ(2S ) → η b (1S )γ transition. The η b (1S ) width is fixed to the world-average value, and only the branching fraction and the mass are reported. For the branching fraction measurement, a non-relativistic Breit-Wigner (BW) signal shape is used, like in all previous measurements. The result B(Υ(2S ) → η b (1S )γ) = (6.1 +0.6+0. 9 −0.7−0.6 ) × 10 −4 agrees with the world average [4]. For the mass measurement, the BW shape multiplied by the photon energy to the third power is used.
MeV/c 2 is just between the two groups of measurements mentioned above, consistent with both of them within the uncertainties. If the E 3 γ term is not used, the mass shifts by 2.6 MeV/c 2 to higher values. We conclude that more precise measurement is needed to solve the puzzle of the η b (1S ) mass.

Observation of the Υ(4S ) → Υ(1S )η transition
Both BaBar and Belle observed many decays of the Υ(4S ), Υ(10860) and Υ(11020) states that do not agree with the expectations for pure bottomonium states (for review see, e.g., [5]). Puzzling properties correspond to a violation of the OZI rule and Heavy Quark Spin Symmetry; their explanation might be a contribution of hadron loops or, equivalently, the B hadron admixture in the Υ states. Recently, Belle reported the observation of a new transition, Υ(4S ) → Υ(1S )η , using the 496 fb −1 data sample collected at the Υ(4S ).
To estimate the energy dependence of the e + e − → χ bJ (1P)π + π − π 0 cross section, the 2D fit is not repeated at every scan point. Instead, the number of signal events is counted in the combined χ b1 and χ b2 signal region and background is subtracted using sidebands. The events are not separated into the ω or higher π + π − π 0 mass samples. The resulting cross sections are presented in figure 4. There are three points with very high accuracy; these are the  Figure 4. Fitting to the cross sections of e + e − → π + π − π 0 χ bJ . Red boxes with error bars are the cross sections of e + e − → π + π − π 0 χ bJ and solid blue curve is fitting curve. measurements in the Υ(10860) on-resonance data that were reported by Belle previously [9]. The accuracy is insufficient to conclude whether the production mechanism is resonant, nonresonant or both. Assuming that the mechanism is resonant, the cross sections are fitted using a sum of Breit-Wigner amplitudes to represent the Υ(10860) and Υ(11020) contributions. The fit results are presented in figure 4. Belle finds B(Υ(10860) → χ bJ (1P)π + π − π 0 ) = (2.5 ± 0.6 ± 2.0 ± 0.7) × 10 −3 and B(Υ(11020) → χ bJ (1P)π + π − π 0 ) = (8.7 ± 4.3 ± 6.1 +4.5 −2.5 ) × 10 −3 . These results agree with the expectations of the B hadron loops model [10].
Belle searched also for the e + e − → χ bJ (1P)φ processes in the Υ(11020) region using the data of six scan points and found no significant signal. These processes are expected to be strongly suppressed (factor 10 3 ) compared to the e + e − → χ bJ (1P)ω [10].