Observation of $\Upsilon(2S)\to\gamma \eta_{b}(1S)$ decay

We report the observation of $\Upsilon(2S)\to\gamma\eta_{b}(1S)$ decay based on analysis of the inclusive photon spectrum of $24.7$ fb$^{-1}$ of $e^+ e^-$ collisions at the $\Upsilon(2S)$ center-of-mass energy collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We measure a branching fraction of $\mathcal{B}(\Upsilon(2S)\to\gamma\eta_{b}(1S))=(6.1^{+0.6+0.9}_{-0.7-0.6})\times 10^{-4}$, and derive an $\eta_{b}(1S)$ mass of $9394.8^{+2.7+4.5}_{-3.1-2.7}$ MeV/$c^{2}$, where the uncertainties are statistical and systematic, respectively. The significance of our measurement is greater than 7 standard deviations, constituting the first observation of this decay mode.

We report the observation of Υ(2S) → γη b (1S) decay based on analysis of the inclusive photon spectrum of 24.7 fb −1 of e + e − collisions at the Υ(2S) center-of-mass energy collected with the Belle detector at the KEKB asymmetric-energy e + e − collider. We measure a branching fraction of B(Υ(2S) → γη b (1S)) = (6.1 +0.6+0. 9 −0.7−0.5 ) × 10 −4 , and derive an η b (1S) mass of 9394.8 +2.7+4.5 MeV/c 2 , where the uncertainties are statistical and systematic, respectively. The significance of our measurement is greater than 7 standard deviations, constituting the first observation of this decay mode.
A striking feature of these results is that BaBar and CLEO find m η b (1S) = 9391.1 ± 2.9 MeV/c 2 , whereas Belle measures 9401.6 ± 1.7 MeV/c 2 . This discrepancy is at the level of 3.1 standard deviations (σ). This may be due to experiment-specific systematic effects, or perhaps lineshape distortion in the M1 transition analogous to J/ψ → γη c (1S) [9,10]. There are a large number of η b (nS) (where n = 1 and 2) mass and width predictions from phenomenological quarkonium potential models, non-relativistic QCD, and lattice calculations [11]. Theory predictions of the branching fractions vary widely for Υ(2S) → γη b (1S) decays in the range of (2 − 20) × 10 −4 [12], and the single experimental measurement is (3.9 ± 1.5) × 10 −4 [3]. Further η b (1S) measurements are necessary for resolving these issues, and reducing the experimental uncertainty in order to discriminate between competing theoretical predictions.
In this Letter, we report a new measurement of Υ(2S) → γη b (1S) decay. By examining the inclusive photon spectrum, we identify the energy peak associated with this radiative transition, and use it to determine m η b (1S) and the branching fraction B(Υ(2S) → γη b (1S)). This analysis is based on 24.7 fb −1 of e + e − collision data at the Υ(2S) center-of-mass (CM) energy collected with the Belle detector at the KEKB asymmetricenergy e + e − collider [13]. This data set is equivalent to (157.8 ± 3.6) × 10 6 Υ(2S) events [14], the largest such sample currently in existence. The Belle detector is a large-solid-angle magnetic spectrometer consisting of a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters, a barrel-like arrangement of time-of-flight scintillation counters, and an electromagnetic calorimeter (ECL) comprised of CsI(Tl) crystals. All these are located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. The ECL is divided into three regions spanning θ, the angle of inclination in the laboratory frame with respect to the direction opposite the e + beam. The ECL backward endcap, barrel, and forward endcap, cover ranges of −0.91 < cos θ < −0.65, −0.63 < cos θ < 0.85, and 0.85 < cos θ < 0.98, respectively. An iron flux return located outside of the magnet coil is instrumented with resistive plate chambers to detect K 0 L mesons and muons. The detector is described in detail elsewhere [15]. The data collected for this analysis used an inner detector system with a 1.5 cm beampipe, a 4-layer SVD, and a small-cell inner drift chamber.
A set of event selection criteria is chosen to enhance the η b (1S) signal while reducing backgrounds from poorly detected photons, π 0 decays, nonresonant production, and other Υ decays. These criteria are determined by maximizing the figure of merit S/ √ S + B (where S and B are the number of expected signal and background events, respectively) for each variable under consideration in an iterative fashion. A subset of ∼5% of the total Υ(2S) data is used as the background sample for optimizing the selection. To avoid potential bias, these events are discarded from the final analysis. Large Monte Carlo (MC) samples of simulated Υ(2S) → γη b (1S) events are used as the signal input, assuming the branching fraction from [3]. Particle production and decays are simulated using the EVTGEN [16] package, with PHOTOS [17] for modeling final-state radiation effects, and PYTHIA [18] for inclusive bb decays. The interactions of the decay products with the Belle detector are modeled with the GEANT3 [19] simulation toolkit.
This analysis studies radiative bottomonium transitions based on the energy spectrum of the photons in each event. Photon candidates are formed from clusters of energy deposited in crystals grouped in the ECL. Clusters are required to include more than a single crystal. The ratio of the energy deposited in the innermost 3 × 3 array of crystals compared to the complete 5 × 5 array centered on the most energetic crystal is required to be greater than or equal to 0.925. Clusters must be isolated from the projected path of charged tracks in the CDC, and the associated electromagnetic shower must have a width of less than 6 cm. Due to increased beam-related backgrounds in the forward endcap region, and insufficient energy resolution in the backward one, we consider only clusters in the ECL barrel region for this analysis.
The inclusive photon sample is drawn from events passing a standard Belle definition for hadronic decays. This requires at least three charged tracks, a visible energy greater than 20% of the CM beam energy ( √ s), and a total energy deposition in the ECL between 0.2 √ s and 0.8 √ s. We consider the cosine of the angle θ T between the photon and the thrust axis calculated in the e + e − CM frame as a discriminant. In a given event, the thrust axis is calculated based on all charged particle tracks and photons except the candidate photon. For continuum background events the photon direction tends to be (anti-) aligned along the thrust axis, whereas the distribution for signal events is isotropic. Therefore to reduce this background we require | cos θ T | < 0.85.
To remove backgrounds from π 0 → γγ decays, each photon candidate is sequentially paired with all remaining photon candidates in the event, and vetoed if the resulting invariant mass (M γγ ) is consistent with that of a π 0 (m π 0 ) [20]. In order to improve purity and reduce combinatorial background, a requirement on the minimum energy of the second photon (E γ2 ) is applied. We require E γ2 > 60 MeV, and |M γγ − m π 0 | > 15 MeV/c 2 .
The resulting spectrum of photon energies in the CM frame (E * γ ) is shown in Fig. 1 The visible peaking structures are due to radiative transitions to and from the χ b0,1,2 (1P ) states. This analysis is concerned with the 300 < E * γ < 800 MeV region, indicated by vertical lines. Due to its relative size, an Υ(2S) → γη b (1S) signal expected near 600 MeV is not seen at this scale.
sition will produce a peak in this distribution near 600 MeV. Direct production of Υ(1S) via initial-state radiation (ISR), e + e − γ ISR → Υ(1S), results in a second peak at E * γ ∼547 MeV. A series of three peaks due to χ bJ=0,1,2 (1P ) → γΥ(1S) [21] transitions are centered at ∼391, ∼424, and ∼442 MeV. These peaks are Dopplerbroadened because the χ bJ (1P ) states originate from Υ(2S) → γχ bJ (1P ) decays, and are therefore not at rest in the CM frame to which we boost the photon energy for this analysis. As such, they also overlap one another. These peaking features are all found above a very large, smooth, inclusive photon background that diminishes as energy increases.
The lineshape parameters and efficiencies are determined from the MC samples. The η b (1S) and χ bJ (1P ) transitions are described by a variation on the Crystal Ball function [22]: a bifurcated Gaussian with individual power-law tails on either side. We assume a natural width for the η b (1S) of Γ η b (1S) = 10 +5 −4 MeV [20]. A Gaussian with a low-side power-law tail [22] is used to model the ISR-produced Υ(1S) signal. The underlying background lineshape is parameterized by an exponential function with a sixth-order polynomial. This was selected based on the best fit of 1.7 fb −1 of continuum background data collected at an energy 30 MeV below the Υ(2S) resonance.
With the above selection criteria our efficiency (ǫ) for the peaking processes ranges from 26 to 32%, depending on the mode (Table I). Photon energy resolution in the CM frame varies from approximately 8 to 12 MeV. Both quantities increase with energy.
The photon energy scale and resolution are verified with multiple independent control samples. The Belle Υ(2S) data were collected in two separate time periods with different operating characteristics. We apply an energy scale adjustment in order to ensure correspondence of the χ bJ (1P ) → γΥ(1S) transition energies in both of the periods. To account for differences between MC simulation and data, we fit the energy spectrum with the MC-determined lineshapes for the Υ(2S) → γχ bJ (1P ) and χ bJ (1P ) → γΥ(1S) transitions, allowing the energy scale and resolution to vary in order to reproduce the expected E * γ values [20] of the χ bJ (1P ) peaks in data. We linearly extrapolate the measured energy scale shift and resolution broadening to the η b (1S) energy region, and correct the expected signal lineshape accordingly.
We perform a binned maximum-likelihood fit to data in the region of 300 < E * γ < 804 MeV including all six peaking components and the exponential background. The yields, energy peak values, and background polynomial coefficients are allowed to vary. In χ bJ (1P ) → γΥ(1S) transitions we find the J = 0 component, known to be suppressed compared to the J = 1 and 2 transitions, to be absorbed into the other nearby peaks. We fix the J = 0 peak position in the fit, and measure a yield consistent with zero. The results of the fit are shown in Fig.  2 and summarized in Table I We consider three categories of systematic uncertainties in this analysis: those related to energy calibration, fit parametrization, and all other uncertainties. These are listed in Table II, and are summed in quadrature.
As verification of the energy calibration, we consider a complementary method based on the photon energy in the laboratory frame, similar to previous Belle studies [5,6]. We derive E γ -dependent corrections to the photon energy according to the comparison between MC and data for D * 0 → D 0 (K ± π ∓ )γ, inclusive η → γγ, and exclusive χ b1,2 (1P ) → γΥ(1S)(µ + µ − ) decays. After applying these corrections, only a small remaining resolution broadening, taken as a systematic uncertainty, is required to the related E * γ values to best reproduce the χ bJ (1P ) → γΥ(1S) transitions in data. The η b (1S) results obtained by these two independent methods agree closely (within 0.2 MeV), providing confidence in our assessment of the energy calibration.
Measurement of the ISR peak position is used to estimate the uncertainty of the η b (1S) transition energy. For this purpose, we adopt the symmetrized combination of the statistical uncertainty from the fit and contributions from the world average Υ mass uncertainties [20]. This value is greater than the maximal difference obtained by repeating the analysis under both energy calibration methods and while varying the derived calibration parameters within ±1σ, providing the most conservative bound on this uncertainty.
Alternative parameterizations of the η b (1S) transition lineshape are considered by refitting the data using a Breit-Wigner functional form, including the case with additional E * 3 γ corrections suggested for some quarkonium transitions [10]. The latter leads to a +2.6 MeV shift in interpretation of the η b (1S) transition energy. The fit is repeated with higher-order E * γ contributions considered, but their relative strength cannot be resolved in this anlaysis, and lead to a small additional systematic uncertainty. We account for uncertainty in the natural η b (1S) width by refitting the data according to MC samples generated with the nominal value varied by ±1σ [20]. By comparing χ 2 goodness-of-fit results under a variety of different assumed values in this range, we verify that our data are consistent with this nominal value. We vary the background shape by changing the degree of the polynomial in the exponential to five and seven, and refitting the data. We also repeat the fit with the background shape fixed to the parameters determined by using only the ISR and η b (1S) sidebands: 300 < E * γ < 500 MeV and 650 < E * γ < 800 MeV. The fit is repeated with a χ b0 (1P ) yield fixed to the expected value, and the difference in results from its effect on the background shape is taken as a systematic uncertainty. The systematic effects of fitting with a finer binning of 1 MeV and with an extended range to 900 MeV are also considered.
We assign an overall photon reconstruction efficiency uncertainty of 2.8% based on previous Belle studies of photons in a similar energy range [23]. The uncertainty on the number of Υ(2S) events was determined from a study of hadronic decays to be 2.3% [14]. Derived quantities related to masses and expected CM energies use the world average values and their associated uncertainties [20].
The corrected peak E * γ values of the χ b1,2 (1P ) transitions are in good agreement with the world average values (in parentheses) [20]    efficiency and ECL angular coverage. We measure (28.8 +2.6+4.2 −3.2−2.2 ) × 10 3 Υ(2S) → γη b (1S) events, equivalent to a branching fraction of (6.1 +0.6+0.9 −0.7−0.5 ) × 10 −4 . This is in agreement with the most recent lattice QCD calculation of (5.4 ± 1.8) × 10 −4 [12]. This value is compatible with the previous BaBar measurement of (3.9±1.5)×10 −4 [3]. We measure a transition energy of E * γ = 606.1 +2.3+3.6 −2.4−3.4 MeV, to be compared with 609.3 +5.0 −4.9 MeV in the similar decay mode in BaBar. If we consider a transition lineshape proportional to E * 3 γ , unlike previous analyses of the M1 radiative transition [2][3][4], the interpretation of the data produces a mass measurement of m η b (1S) = 9394.8 +2.7+4.5 −3.1−2.7 MeV/c 2 . This is in agreement with the current world average value of 9399.0 ± 2.3 MeV/c 2 [20]. This is between previous Belle h b -based measurements [5,6] and those from radiative Υ decays [2][3][4], consistent with the former at the level of 1.2σ, and 0.7σ for the latter. The statistical significance of this measurement is estimated to be 8.4σ, determined from the difference in the likelihood between the results with and without an η b (1S) component included. Even after considering yield-related systematic uncertainties, the signal significance exceeds 7σ. This result represents the first significant observation of the Υ(2S) → γη b (1S) decay mode. We look forward to additional dedicated bottomonium data samples from the Belle II experiment to mitigate energy scale uncertainties and provide greater ability to interpret radiative M1 transition lineshape effects.