Bottomonium states (bound states of b b) above the B B threshold have unexpected properties. For example, the ϒð10860Þ resonance, commonly denoted as ϒð5SÞ, decays into ϒðnSÞπ þ π -(n ¼ 1, 2, 3) with widths around 300-400 keV, about 2 orders of magnitude larger than those for similar decays of the ϒð2SÞ -ϒð4SÞ which have widths around 0.5-5 keV [1]. One possible interpretation of such behavior is the existence of a light-flavor admixture in the ϒð5SÞ resonance [2,3].
Observation by the Belle collaboration of unexpectedly large values for the ratios 07 -0.12 and Γðϒð5SÞ→h b ð2PÞπ þ π -Þ Γðϒð5SÞ→ϒð2SÞπ þ π -Þ ¼ 0.77 AE 0.08 þ0.22 -0.17 [4], predicted to be Oð10 -2 Þ due to heavy quark spin flip [5], led to discovery of the exotic four-quark bound states, Z b ð10610Þ and Z b ð10650Þ [6]. A similar ratio, Γðϒð4S;5SÞ→ϒð1SÞηÞ Γðϒð4S;5SÞ→ϒð1SÞπ þ π -Þ , is also expected to be Oð10 -2 Þ in the QCDME model [7] but has been measured to be 2.41 AE 0.40 AE 0.12 for the ϒð4SÞ [8]. Moreover, the measurement of Bðϒð4SÞ → ηh b ð1PÞÞ ¼ ð2.18 AE 0.11 AE 0.18Þ × 10 -3 [9] violates naive quark-antiquark models [10] like QCDME. Nevertheless, for bottomonium states below the B B threshold, the QCDME model predictions are consistent with measurements: [11]. Therefore, analysis of similar processes will be crucial for a better understanding of the quark structure of bottomonium states above the B B threshold.
This paper describes the study of hadronic transitions between bottomonium states with emission of an η ð0Þ meson at ffiffi ffi s p ¼ 10.866 GeV. The process e þ e -→ ϒð2SÞη is studied in two different modes: the first, ϒð2SÞ → ϒð1SÞπ þ π -, ϒð1SÞ → μ þ μ -, η → γγ, denoted as ϒð2SÞη½γγ and the second,
The process e þ e -→ ϒð1SÞη is studied in the decay chain ϒð1SÞ → μ þ μ -, η → π þ π -π 0 , π 0 → γγ, denoted as ϒð1SÞη½3π. The process e þ e -→ ϒð1SÞη 0 is studied in two different modes: the first, ϒð1SÞ → μ þ μ -, η 0 → π þ π -η, η → γγ, denoted as ϒð1SÞη 0 ½ππη and the second, ϒð1SÞ → μ þ μ -, η 0 → ρ 0 γ, ρ 0 → π þ π -, denoted as ϒð1SÞη 0 ½ργ. The ϒð1SÞη 0 ½ργ mode is the only process with a μ þ μ -π þ π -γ final state, while the others lead to μ þ μ -π þ π -γγ in the final state.
The first evidence for e þ e -→ ϒð2SÞη was reported in Ref. [12], measured through the recoil mass distribution against η mesons. The Born cross section [see Eq. (3)] was found to be σ B ðe þ e -→ ϒð2SÞηÞ ¼ 1.02 AE 0.30 AE 0.17 pb, and the upper limit σ B ðe þ e -→ ϒð1SÞηÞ < 0.49 pb was set at 90% confidence limit. The results reported here are based on the reconstruction of exclusive decays and are independent of the published results.
We use a data sample of 118.3 fb -1 collected at the ϒð5SÞ resonance and 21 fb -1 collected during a scan of center-of-mass energies in the range 10.63-11.02 GeV by the Belle detector [13,14] at the KEKB asymmetric-energy e þ e -collider [15,16]. The average center-of-mass (c.m.) energy of the ϒð5SÞ sample is ffiffi ffi s p ¼ 10.866 GeV. The Belle detector was a large-solid-angle magnetic spectrometer that consisted of a silicon vertex detector, a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters, and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL) located inside a superconducting solenoid coil that provided a 1.5 T magnetic field. An iron flux-return yoke located outside of the coil (KLM) was instrumented to detect K 0 L mesons and to identify muons.
Event selection requirements are optimized using a full Monte Carlo (MC) simulation. MC events are generated using EvtGen [17] and the detector response is modeled using GEANT3 [18]. In the simulation of e þ e -→ ϒð1S; 2SÞη ð0Þ we use the angular distribution dictated by the quantum numbers for a vector decay to a pseudoscalar and a vector. The dimuon decay of ϒð1S; 2SÞ is simulated to be distributed uniformly in phase space, taking into account the proper spin dynamics for decay of a massive vector meson to two leptons. For ϒð2SÞ → ϒð1SÞπ þ π -, we use a dipion invariant mass distribution according to the Voloshin and Zakharov model [5] measured in [19]. For the η → π þ π -π 0 decay, final state particles are distributed in phase space according to the model from [20]. Other decays are generated uniformly in phase space. Final-state radiation is taken into account using the PHOTOS package [21]. The simulation also takes into account variations of the detector configuration and beam conditions.
The event selection is performed in two steps. First we require the presence of at least two oppositely charged muon and two oppositely charged pion candidates. Charged tracks must originate from a cylindrical region within AE2.5 cm along the z axis (opposite the positron beam) and 2 cm in the transverse direction, relative to the e þ e -interaction point. Muon candidates are identified with a requirement on a likelihood ratio P μ ¼ L μ L μ þL π þL K > 0.1 (efficiency is ≈99.9%), where the likelihood L i , with i ¼ μ, π, K, is assigned based on the range of the particle extrapolated from the CDC through KLM and on the deviation of hit positions from the extrapolated track [22]. Every charged particle that is not identified as a muon or an electron (P e < 0.99) is considered to be a charged pion, where P e is a similar likelihood ratio based on CDC, ACC, and ECL information [23]. Additionally, we require the dimuon invariant mass M μμ to satisfy 8 GeV=c 2 < M μμ < 12 GeV=c 2 and dipion invariant mass M ππ < 4 GeV=c 2 . At this stage, no requirements on photon candidates are applied.
Final-state-specific requirements are applied at the second stage. The following set of selection variables are common to all processes: the angle Ψ between the total momentum of the photons and the total momentum of the charged particles in the e þ e -c.m. frame, the invariant mass of the muon pair M μμ [corresponding to the ϒð1S; 2SÞ], and the total reconstructed energy of the final-state particles, E tot . These variables are used to select exclusive decay chains that result in the same final states μ þ μ -π þ π -γðγÞ.
The signal region for ϒð1SÞ → μ þ μ -is defined to be 9.235 GeV=c 2 < M μμ < 9.685 GeV=c 2 and that for ϒð2SÞ → μ þ μ -is 9.76 GeV=c 2 < M μμ < 10.28 GeV=c 2 . Four-momentum conservation requires the angle Ψ to be equal to π radian; however, it can deviate even for true candidates due to finite momentum and energy resolutions. For the ϒð2SÞη½3π mode this effect results in a less strict requirement on the angle Ψ due to the low momentum of the π 0 . Selection criteria for the angle Ψ are listed in Table I for all modes. If multiple candidates occur in an event, usually due to additional photons from background processes, the μμππγðγÞ combination with Ψ closest to π radians is chosen as the best candidate. According to the simulation, the fraction of events containing multiple candidates is ≈24% for the ϒð2SÞη½3π mode and ranges from 3% to 12% for other modes. Finally, E tot is calculated as
where, instead of the reconstructed value of the μ þ μ --pair invariant mass, the world-average mass of the ϒ meson is used [1]. This approach allows one to improve the E tot resolution by removing the contribution from the M μμ resolution, whose value is about 50 MeV=c 2 and To reconstruct a neutral pion from the π 0 → γγ decay in the ϒð1S; 2SÞη½3π modes, the invariant mass M γγ must be in the signal range 110 MeV=c 2 < M γγ < 155 MeV=c 2 , where the resolution is 5.5 MeV=c 2 . For the ϒð1SÞη 0 ½ππη mode the η meson is reconstructed from the η → γγ decay with a signal range 450 MeV=c 2 < M γγ < 625 MeV=c 2 , where the resolution is 12.3 MeV=c 2 . For the ϒð1SÞη 0 ½ργ mode the ρ 0 resonance is reconstructed from the
For the two-body ϒð5SÞ → ϒð2SÞη½γγ decay the η meson is monochromatic, with a c.m. momentum equal to 615 MeV=c. Thus, the photons produced in a η → γγ decay have an energy distributed in the range 105-715 MeV in the c.m. frame. We require the photon energy to be greater than 100 MeV, which significantly reduces combinatorial background and has virtually no effect on signal events.
For the ϒð2SÞη½γγ final state the ϒð2SÞ meson is reconstructed via its decay chain ϒð2SÞ → ϒð1SÞπ þ π - with ϒð1SÞ → μ þ μ -. We calculate the mass difference M μμππ -M μμ ¼ δM, where the correlated contributions to resolution from the muon momentum measurement substantially cancel. The peak of δM corresponds to ΔM ¼ M ϒð2SÞ -M ϒð1SÞ ¼ 562 MeV=c 2 , and the resolution is approximately 4.6 MeV=c 2 . A requirement of jδM -ΔMj < 18 MeV=c 2 is applied.
For all modes, the signal is found by fitting the M η ð0Þ (M γγ , M ππγγ or M ππγ ) invariant mass distribution, as it has no peaking background (see Sec. III). The MC signal distribution is taken as a sum of a Crystal Ball function [24] and a Gaussian. The reconstruction efficiency ε is then determined as N det =N gen , where N det is the integral of the fitted function and N gen ¼ 10 6 . Results are summarized in Table I.
The most relevant background to this analysis comes from transitions between other bottomonium states with emission of an η ð0Þ . Such decays have an η ð0Þ invariant mass distribution identical to our signal modes.
Due to the η 0 mass and parity considerations, the η 0 meson can originate only from the ϒð5SÞ → ϒð1SÞη 0 decay or from ϒð5SÞ → χ bJ ð1PÞη 0 γ decays with a subsequent radiative decay χ bJ ð1PÞ → ϒð1SÞγ. The former is our signal and the latter is suppressed by the presence of an additional photon.
In contrast, the η meson can also originate from ϒð5SÞ → ϒð1DÞη [12] and ϒð5SÞ → ϒð2S; 3SÞX followed by ϒð2S; 3SÞ → ϒð1SÞη decays. For the ϒð5SÞ → ϒð1DÞη decay, the most relevant channels are those with ϒð1DÞ → χ bJ γ → ϒð1SÞγγ and ϒð1DÞ → ϒð1SÞπ þ π -decays. However, the first decay chain has two extra photons in the final state and is suppressed by the requirement on E tot . The second decay might produce a correct set of finalstate particles (with η → γγ), but is significantly suppressed by the requirement on M μμππ -M μμ : for the ϒð1DÞ → ϒð1SÞπ þ π -decay, this variable peaks in δM at approximately 140 MeV=c 2 higher than for the ϒð2SÞ → ϒð1SÞπ þ π -with a resolution of about 5 MeV=c 2 . Therefore, the ϒð1DÞ → ϒð1SÞπ þ π -signal fails our criteria and is completely eliminated.
The decay chain ϒð5SÞ → ϒð2S; 3SÞπ þ π -, ϒð2S; 3SÞ → ϒð1SÞη, η → γγ produces the same set of final-state particles and the same signal distribution as the ϒð2SÞη½γγ mode. However, the branching fractions Bðϒð2S; 3SÞ → ϒð1SÞηÞ are small, and with the current integrated luminosity the expected number of η mesons produced by this mechanism is estimated to be 2 for the ϒð2SÞ and less than 1 for the ϒð3SÞ. Contributions from these decays are also strongly suppressed by the requirement on M μμππ -M μμ ; its mean value deviates from the ϒð2SÞ → ϒð1SÞπ þ π -signal window by 280 MeV=c 2 and 50 MeV=c 2 for ϒð5SÞ → ϒð2SÞπ þ π - and ϒð5SÞ → ϒð3SÞπ þ π -, respectively.
A possible source of background for ϒð5SÞ → ϒð2SÞη is from the decay itself, with ϒð2SÞ → ϒð1SÞη,
This final state is similar to the ϒð2SÞη½γγ mode when a soft photon or π 0 is undetected. Nevertheless, this background is negligible due to the small branching fraction,
, and requirements on E tot . Crossfeed between the signal modes is a source of background that passes the common selection criteria but does not produce peaks in the signal distributions. For the ϒð1SÞη½3π and ϒð1SÞη 0 modes, there is such a background from the ϒð2SÞη½γγ mode when ϒð2SÞ → ϒð1SÞπ þ π -. To reduce this background for the ϒð1SÞη ð0Þ mode, we require jM μμππ -M μμ -ðM ϒð2SÞ -M ϒð1SÞ Þj> 10MeV=c 2 , which only slightly decreases the signal reconstruction efficiency and suppresses this background to a negligible level. The crossfeed between the ϒð1SÞη½3π and ϒð2SÞη½3π modes is efficiently removed by the common selection requirements.
Another significant part of the background is the nonpeaking combinatorial background. To evaluate the expected level, we used a set of MC events equivalent to 6 times the integrated luminosity of the data and including the following processes: e þ e -→ cc, u ū, d d, ss; e þ e -→ B ðÃÞ s
s , B ðÃÞ BðÃÞ ðπÞ; and known decays of the ϒð5SÞ. In addition, we performed a simulation of e þ e -→ τ þ τ -events with statistics equivalent to the integrated luminosity of our dataset. The only events remaining after the application of our selection criteria originate from ϒð5SÞ decays to final states containing bottomonium. For example, the dominant background to the ϒð2SÞη½γγ comes from the ϒð2SÞπ 0 π 0 final state, which produces a broadly peaking M γγ distribution from 50 to 850 MeV=c 2 with a maximum near the signal η peak position. To suppress this background, we tightened the requirement on the total reconstructed energy from 10.75 to 10.80 GeV for the ϒð2SÞη½γγ mode. This reduces the expected number of background events for the ϒð2SÞη½γγ from 20 to 5 events and slightly decreases the detection efficiency.
For the ϒð1SÞη 0 ½ργ mode, the MC study predicts a high background from the ϒð5SÞ → ϒð2SÞπ þ π -decay, where ϒð2SÞ → μ þ μ -γðγÞ. To reduce this background we set a veto on the recoil mass M rec ππ : jM rec ππ -M ϒð2SÞ j > 20 MeV=c 2 . The MC study also predicts background contributions from decays with the ϒð2S; 3SÞ → ϒð1SÞ½μ þ μ -π þ π -intermediate transition. Therefore, we reduced this background in the same way as for the ϒð1SÞη½3π and ϒð1SÞη 0 ½ππη modes by setting vetoes jM μμππ -M μμ -ðM ϒð2S;3SÞ -M ϒð1SÞ Þj > 10 MeV=c 2 . Moreover, there are no requirements on photons except the general one from four-momentum conservation, therefore we expect background from low-energy photons. To suppress this background we set a minimum photon energy in the c.m. frame of E Ã γ > 80 MeV. This requirement reduces the reconstruction efficiency by factor of 1.12, and greatly reduces background.
We find that all these sources, predicted by the background MC, account for less than 30% of the observed background in the sideband data. The remainder of the background is thought to originate from QED processes that, in general, have much higher cross sections, e.g.,
. This e þ e - pair could be reconstructed as a pair of collinear pions. A selection requirement on the opening angle between two charged pion candidates of α ππ > 0.18 radian for the ϒð1SÞη½3π mode and of α ππ > 0.3 radian for the ϒð2SÞη½3π mode reduces this background substantially.
Finally, we tested for possible background from nonresonant e þ e -→ μ þ μ -η ð0Þ decays using experimental data with the requirement on M μμ shifted to central values ranging from 8 to 9 GeV=c 2 , i.e., lower than the ground bottomonium state. No evidence for such processes was observed.
The signal yield is determined from a binned maximum likelihood fit to the invariant mass M η ð0Þ (M γγ , M ππγγ or M ππγ ) distribution (Figs. 1 and2), with the fitting function being the sum of the signal function and a background function ðxp 1 Þ p 2 e p 3 x , where p 1 , p 2 , p 3 are floating parameters. All parameters of the signal function, except its normalization factor and the Crystal Ball peak position, are fixed to the values determined from the fit to the MC distribution, with the difference in position between Crystal Ball and Gaussian peaks being fixed.
The visible cross section is
where N sig is the fitted signal yield, L is the integrated luminosity, B is the product of the intermediate branching fractions for the process, and ε is the reconstruction efficiency. For the ϒð2SÞη½γγ, ϒð2SÞη½3π, and ϒð1SÞη½3π modes we evaluate the signal significance as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2 log ½LðNÞ=Lð0Þ p , where LðNÞ=Lð0Þ is the ratio between the likelihood values for a fit that includes a signal yield N and a fit with a background hypothesis only. The calculated significances are 12.8σ, 10.5σ, and 10.2σ, respectively. Thus, we report the first observation of the e þ e -→ ϒð2SÞη process in both modes and the first observation of the e þ e -→ ϒð1SÞη process at ffiffi ffi s p ¼ 10.866 GeV. Setting the requirement 520 < M η < 580 MeV, we also confirm that there are clear peaks in M μμ distributions (Fig. 3), consistent with ϒð1S; 2SÞ → μ þ μ -, for these modes.
For the ϒð1SÞη 0 ½ππη and the ϒð1SÞη 0 ½ργ modes the signal yield is N sig ¼ -1.76 AE 3.30 and N sig ¼ 3.30 AE 4.41 respectively; upper limits are set using a pseudo-experiment method. In this method we simulate 10 5 trials, for which background number of events is distributed according to the Poisson distribution with the mean matching the number observed in the data and the signal events generated with a given signal yield. A value of M ππγðγÞ is generated according to the background line shape obtained from the fit to the data for each background event, and according to MC signal shape for each signal event.
Then, the M ππγðγÞ distribution for each trial is fitted using the same procedure as with data, and the obtained signal yield is recorded. A confidence limit, C.L., is calculated from the distribution of the fit results as a fraction of events with the signal yield exceeding N sig obtained from the fit to the data. Repeating the procedure for several generated signal yield values, 90% C.L. signal yield is obtained from C.L. vs generated signal yield curve. As a result, the 90% C.L. upper limits for the ϒð1SÞη 0 ½ππη and ϒð1SÞη 0 ½ργ modes are found to be N sig ¼ 2.1 and N sig ¼ 8.3, respectively.
Table II shows the signal yields, calculated visible cross sections, and peak positions for the η meson, which are consistent with the world-average value M η ¼ 547.86 AE 0.02 MeV=c 2 [1] within the statistical uncertainty.
We study the cross section behavior of the processes below the ϒð5SÞ to estimate radiative corrections. For this study we use 21 fb -1 of data collected at c.m. energies from 10.63 to 11.02 GeV. We group these data into three energy bands: 10.63-10.77 GeV (A), 10.83-10.91 GeV (B) and 10.93-11.02 GeV (C). They are analyzed in the same way as the data on the ϒð5SÞ except for the requirement on E tot , which is shifted to the corresponding CMS energy. This analysis shows (Table III) that there are no signal events in band A except for one event in the ϒð2SÞη½3π and ϒð1SÞη 0 ½ργ modes. For each mode we set upper limits N sig < 1 corresponding to a C.L. of 63%.
For the ϒð1SÞη½3π, ϒð1SÞη 0 ½ππη, and ϒð1SÞη 0 ½ργ modes, the upper limits are higher than the values measured at the ϒð5SÞ resonance, while for the e þ e -→ ϒð2SÞη process the upper limit indicates resonance production of the final state. Since resonance production has been observed in similar processes e þ e -→ ϒð1S; 2S; 3SÞπ þ π - [25,26] and e þ e -→ h b ð1P; 2PÞπ þ π - [27], and our new results do not rule it out, we assume a resonance model to calculate the radiative correction for all modes as described, for example, in [28], neglecting the possible energy dependence of the resonance width. For this calculation, the following ϒð5SÞ parameters are used: M ϒð5SÞ ¼ 10885.2 MeV=c 2 , Γ ϒð5SÞ ¼ 37 MeV [1]. We calculate radiative correction 1 þ δ to vary from 0.624 to 0.628 for different modes. This correction is used to calculate the Born cross section (σ B ) as
where j1 -Πj 2 ¼ 0.929 is the vacuum-polarization factor [12,29].
The particle reconstruction efficiency and particle identification are important parameters whose values in simulation could differ from those in the experiment. According to independent studies, for example using the D Ã-→ π -D0 ½K 0 S π þ π -decay, the systematic uncertainty due to track reconstruction is 1% for pions and 0.35% for high-momentum muons [30]. The photon reconstruction uncertainty is 1.5%. The muon identification uncertainty is 1%, according to analysis of J=ψ → μ þ μ - [30]. Therefore, the total systematic uncertainty for the
final states is 2.7% from charged track reconstruction, 1.5% and 3% respectively from photon reconstruction and 2% from muon identification.
Another uncertainty can come from the accuracy of the PHOTOS module, which describes final-state radiation. To evaluate this uncertainty we simulate the ϒð2SÞη½γγ and ϒð2SÞη½3π modes without the PHOTOS module. For both processes the cross section increases by 9% mostly due to the absence of radiation by muons, which could account for hundreds of MeV of energy. Thus, the total influence of PHOTOS on the efficiency is 9% while its own uncertainty is a few percent [21]; therefore, the uncertainty on the detection efficiency appears in the next order and we take 1% as a conservative estimate.
The dependence of the cross section on c.m. energy could differ from a pure Breit-Wigner. As an alternative dependence we add to the ϒð5SÞ Breit-Wigner a constant contribution with an amplitude derived from the upper limit of 0.45 pb found in band A (see Table III).
The upper limit of 0.45 pb corresponds to 0.58 pb after applying the correction for initial-state radiation. Considering this to be a constant contribution to the Born cross section and using the visible cross section of 1.39 pb at ffiffi ffi s p ¼ 10.866 GeV (Table II), we estimate that the corrected cross section at ffiffi ffi s p ¼ 10.866 GeV is 2.10 pb, thus the constant component constitutes a fraction 0.58=2.10 ¼ 0.276. Using this cross section dependence, we calculate a radiative correction for all modes. Its deviation from the nominal values ranges from 4.3% to 5.7% and is referred to as the radiative correction uncertainty.
To estimate the influence of selection criteria we vary three unified requirements: the width of the E tot signal range is symmetrically varied by AE60 MeV from the nominal value, the lower boundary for the angle Ψ is varied from 2 to 2.8 radians, and the width of the M μμ signal range is symmetrically varied by AE200 MeV=c 2 from the nominal value. The maximum cross section deviation from the nominal is taken as a systematic uncertainty. The total uncertainty due to selection criteria is the quadratic sum of these three contributions and is shown in Table IV.
One more indication of systematic error is the deviation between simulated and experimental resolutionsexperimental distributions are usually wider than those in simulation. To estimate the uncertainty from this source, we choose events with the ϒð1SÞ originating from ϒð2SÞ → ϒð1SÞπ þ π -, using the requirement jM μμππ -M μμ -ðM ϒð2SÞ -M ϒð1SÞ Þj < 18 MeV=c 2 . Parametrization of the experimental M μμ distribution with a sum of a Gaussian and linear function finds a resolution of 54 AE 1.5 MeV=c 2 , which is larger than the resolution in MC of 50 MeV=c 2 by 8%. This deviation is common for other distributions; therefore, we vary the resolution of the signal M η ð0Þ distribution by AE10% to evaluate the reconstruction efficiency in MC and fit to the experimental data. The maximum deviation of the cross section from the nominal one is referred to as the resolution uncertainty. Additionally, we verified that the data parametrization with floating resolution is consistent with the simulation within the statistical uncertainty.
The uncertainty due to signal line shape is taken as the maximum difference of the cross section between data fits with different signal parametrizations. The nominal line shape is the sum of the Crystal Ball function and a Gaussian, while two tested alternate line shapes are a Gaussian only and a Crystal Ball only. The uncertainty due to background line shape is the maximum difference of the cross section between fits to the data in different signal ranges-in this way not every background event is included in the fit and the background line shape changes.
The η 0 → π þ π -η decay was simulated uniformly in phase space, which is not necessarily the correct representation of dynamics of this process. However, Ref. [31] shows that experimental Dalitz distributions are consistent with a uniform distribution over phase space; thus, this source of uncertainty is neglected.
The bin width of the fitted distribution in M η ð0Þ is 10 MeV=c 2 . The uncertainty due to binning is estimated by refitting the data with bin widths of 5, 8 and 12 MeV=c 2 .
The uncertainty in integrated luminosity is 1.4%. The uncertainties of the intermediate branching fractions are given in Table V. For the ϒð1SÞη 0 ½ππη and ϒð1SÞη 0 ½ργ modes, some of the uncertainties cannot be evaluated due to zero signal yield. Such uncertainties are assumed to be equal to those in the ϒð1SÞη½3π mode. The total uncertainty is evaluated as the quadratic sum from all sources.
To validate the analysis procedure we measure the known process e þ e -→ ϒð2SÞπ þ π -, where ϒð2SÞ is reconstructed via the decay chain ϒð2SÞ → χ bJ ð1PÞγ, χ bJ ð1PÞ → ϒð1SÞγ, ϒð1SÞ → μ þ μ -, and J ¼ 0, 1, 2. The cross section for this process is measured independently with the ϒð2SÞ → μ þ μ -decay where the statistics of signal events is much higher [30].
The analysis procedure is almost the same as for the other modes. Selection criteria for this process are based on the same set of common variables: ϒð1SÞ meson is reconstructed by the M μμ in the 9.235 GeV=c 2 < M μμ < 9.685 GeV=c 2 range, the angle Ψ > 2.6 radian, and the total reconstructed energy 10.75 GeV < E tot < 10.94 GeV. In addition, a requirement on the mass recoiling off two charged pions, M rec ππ , is applied as jM rec ππ -M ϒð2SÞ j < 30 MeV=c 2 . According to MC simulation, the resolution of M rec ππ is 6 MeV=c 2 . This helps to reduce background from the e þ e -→ ϒð1DÞπ þ π -process, where ϒð1DÞ → χ bJ γ, χ bJ ð1PÞ → ϒð1SÞγ.
Each candidate event contains two μ þ μ -γ combinations. The one with the larger value of M μμγ -M μμ is taken to be the candidate for χ bJ ð1PÞ → ϒð1SÞγ. The studied process results in peaks at 399.1, 432.5, and 451.9 MeV=c 2 for J ¼ 0, 1, 2, respectively. Distributions for each χ bJ ð1PÞ are fitted to the sum of a Crystal Ball function and a Gaussian in the same way as for the other processes. Reconstruction efficiencies are ε χ b0 ð1PÞ ¼ 28.12 AE 0.04%, ε χ b1 ð1PÞ ¼ 28.68 AE 0.04%, and ε χ b2 ð1PÞ ¼ 28.52 AE 0.04%.
The known products of the intermediate branching fractions B χ bJ ð1PÞ ¼ Bðϒð2SÞ → χ bJ ð1PÞγÞ × Bðχ bJ ð1PÞ → ϒð1SÞγÞ are B χ b0 ð1PÞ ¼ ð7.37 AE 1.28Þ × 10 -4 , B χ b1 ð1PÞ ¼ ð242 AE 19Þ × 10 -4 , and B chib2ð1PÞ ¼ ð128 AE 9Þ × 10 -4 [1]. The relative contributions to the signal, ε χ bJ ð1PÞ × B χ bJ ð1PÞ , for J ¼ 0, 1, 2 are in the ratios 0.029∶1∶0.527. The total MC signal line shape is the sum of three contributions, with all parameters except an overall normalization factor being fixed for the data analysis. The total branching fraction weighted with the efficiency is
Bðχ bJ ð1PÞ → ϒð1SÞγÞ ¼ ð2.69 AE 0.16Þ × 10 -4 , and is used to calculate the cross section [Eq. ( 2)].
Figure 4 shows the experimental M μμγ -M μμ distribution. The signal yield is determined from fitting the M μμγ -M μμ distribution, with the fit function being the sum of the total MC signal line shape and a background function ðx-p 1 Þ p 2 e p 3 x . We obtain N sig ¼85.32AE11.5, resulting in the Born cross section σ B ðe þ e -→ϒð2SÞπ þ π -Þ¼ 3.98AE0.54pb (statistical uncertainty only). This value is consistent with the independent measurement σ B ðe þ e -→ ϒð2SÞπ þ π -Þ ¼ 4.07 AE 0.16 AE 0.45 pb [30] within the uncertainty.
In summary, using the Belle data sample of 118.3 fb -1 obtained at ffiffi ffi s p ¼ 10.866 GeV, we report measurements of the cross sections for the processes e þ e -→ ϒð1S; 2SÞη, and set an upper limit on the cross section of e þ e -→ ϒð1SÞη 0 . The measured Born cross sections, with initial-state radiation being taken into account, are [Eq. (
The weighted averages for the corresponding modes are σ B ðe þ e -→ ϒð2SÞηÞ ¼ 2.07 AE 0.21 AE 0.19 pb, σ B ðe þ e -→ ϒð1SÞηÞ ¼ 0.42 AE 0.08 AE 0.04 pb, σ B ðe þ e -→ ϒð1SÞη 0 Þ < 0.037 pb, C:L: ¼ 90%.
The significances exceed 10σ for e þ e -→ ϒð1SÞη and e þ e -→ ϒð2SÞη, and we claim first observations of these processes. For e þ e -→ ϒð2SÞη, our measured cross section is statistically consistent with the previous result [12] within ∼2.3σ. Such a discrepancy can be accounted for by statistical fluctuation. For e þ e -→ ϒð1SÞη, our result is consistent with the published result.
Under the assumption that these processes proceed only through the ϒð5SÞ, we calculate branching fractions with the formula Bðϒð5SÞ→XÞ¼σ vis ðe þ e -→XÞ=σðe þ e -→ ϒð5SÞÞ, where σ vis ðe þ e -→ϒð5SÞÞ¼0.340AE0.016nb [32]: Bðϒð5SÞ → ϒð1SÞηÞ ¼ ð0.85 AE 0.15 AE 0.08Þ × 10 -3 , Bðϒð5SÞ → ϒð2SÞηÞ ¼ ð4.13 AE 0.41 AE 0.37Þ × 10 -3 , Bðϒð5SÞ → ϒð1SÞη 0 Þ < 7.3 × 10 -5 , C:L: ¼ 90%.
Using σðe þ e -→ ϒð1SÞπ þ π -Þ ¼ 2.27 AE 0.12 AE 0.14 pb, σðe þ e -→ ϒð2SÞπ þ π -Þ ¼ 4.07 AE 0.16 AE 0.45 pb [30] and the obtained Born cross section, we also calculate the width ratios between η and dipion transitions to be where correlated systematic uncertainties cancel in the ratio. These values are significantly larger than the predicted values of ∼0.03 for ϒð2SÞ and ∼0.005 for ϒð1SÞ, calculated in the QCDME regime [5], and may be compared to ϒð4SÞ→ϒð1SÞη ϒð4SÞ→ϒð1SÞπ þ π -¼ 2.41 AE 0.40 AE 0.12 [8], measured in a regime where QCDME is no longer valid. Similarly, our measured upper limit on the ratio between the η 0 and η transitions is Γðϒð5SÞ → ϒð1SÞη 0 Þ Γðϒð5SÞ → ϒð1SÞηÞ < 0.10 ðC:L: ¼ 90%Þ; ð6Þ which is significantly smaller than the value ≈12 predicted by the naive QCDME model [2].
As shown in Refs. [2,3], a suggested solution is the existence of a light-flavor admixture to the b b state. Such a structure of the ϒð5SÞ resonance could result in a larger cross section for e þ e -→ ϒð1S; 2SÞη and e þ e -→ ϒð1SÞη 0 processes and lead to dominance of the e þ e -→ ϒð1S; 2SÞη process over e þ e -→ ϒð1SÞη 0 [3]:
still higher than the obtained limit. Such suppression has also been observed in Ref. [33], where Γðϒð4SÞ→ϒð1SÞη 0 Þ Γðϒð4SÞ→ϒð1SÞηÞ is reported to be 0.20 AE 0.06, in agreement with the expected value in the case of an admixture of a state containing light quarks.