Observation of $\Upsilon(4S)\to \eta' \Upsilon(1S)$

We report the first observation of the hadronic transition $\Upsilon(4S)\to\eta'\Upsilon(1S)$, using 496 fb$^{-1}$ data collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider. We reconstruct the $\eta'$ meson through its decays to $\rho^0\gamma$ and to $\pi^+\pi^-\eta$, with $\eta\to\gamma\gamma$. We measure: ${\cal B}(\Upsilon(4S)\to\eta'\Upsilon(1S))=(3.43\pm 0.88 {\rm(stat.)} \pm 0.21 {\rm(syst.)})\times10^{-5}$, with a significance of 5.7$\sigma$.

We report the first observation of the hadronic transition Υ(4S) → η Υ(1S), using 496 fb −1 data collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. We reconstruct the η meson through its decays to ρ 0 γ and to π + π − η, with η → γγ. We measure: B(Υ(4S) → η Υ(1S)) = (3.43 ± 0.88(stat.) ± 0.21(syst.)) × 10 −5 , with a significance of 5.7σ. PACS numbers: 14.40.Pq,13.25.Gv One of the major challenges in particle physics is the treatment of non-perturbative QCD [1]. Quarkonia, thanks to their intrinsic multi-scale behavior, are one of the most promising and clean laboratories in which to explore these dynamics [2]. In particular, hadronic transitions between bottomonia have been, in the past few years, a fertile field for both experiment and theory. On the basis of heavy quark spin symmetry, the QCD multipole expansion (QCDME) model predicts that η transitions should be suppressed relative to dipion transitions [3]. Several recent results [4][5][6][7] challenge this longstanding expectation. Following these measurements, it has been argued that the light-quark degrees of freedom actively intervene in the transitions [8].
Few processes for the Υ(4S) decaying to the non-BB system have been measured thus far [9]. There have been no searches for the kinematically allowed transition Υ(4S) → η Υ(1S) , which is expected to be enhanced just as Υ(4S) → ηΥ(1S) [8], where the relative strength of the η and η transitions depends on the relative uū + dd content of the mesons, and is predicted to range between 20 and 60%. In contrast, a significant dominance of the η transition is predicted by QCDME models. In the charmonium sector, searches for ψ(4160) → η J/ψ and Y (4260) → η J/ψ transitions have been made by CLEO [10] without observation of significant signals, while the observation of e + e − → η J/ψ at center-of-mass energy of 4.226 GeV and 4.258 GeV has been reported by BESIII [11].
In this Letter, we present the first observation of the transition Υ(4S) → η Υ(1S). The Υ(1S) meson is reconstructed via its leptonic decay to two muons, which is considerably cleaner than the di-electron mode. The η meson is reconstructed via its decays to ρ 0 γ and to π + π − η, with the η meson reconstructed as two photons.
We use a sample of (538 ± 8) × 10 6 Υ(4S) mesons, corresponding to an integrated luminosity of 496 fb −1 , collected by the Belle experiment at the KEKB asymmetricenergy e + e − collider [12,13]. In addition, a data sample corresponding to 56 fb −1 , collected about 60 MeV below the resonance, is used to estimate the background contribution.
The Belle detector (described in detail elsewhere [14,15]) is a large-solid-angle magnetic spectrometer that consists 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 super-conducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return located outside of the coil (KLM) is instrumented to detect K 0 L mesons and to identify muons.
Monte Carlo (MC) simulated events are used for the efficiency determination and the selection optimization; these are generated using EvtGen [16] and simulated to model the detector response using GEANT3 [17]. The changing detector performance and accelerator conditions are taken into account in the simulation. The distributions of generated dimuon decays incorporate the Υ(1S) polarization. The angular distribution in the Υ(4S) → η Υ(1S) transition is simulated as a vector decaying to a pseudoscalar and a vector. The η → π + π − η and the η → γγ decays are generated uniformly in phase space, while the η → ρ 0 γ → π + π − γ decay is generated assuming the appropriate helicity. Final state radiation effects are modeled in the generator by PHOTOS [18].
Charged tracks must originate from a cylindrical region of length ±5 cm along the z axis (opposite the positron beam) and radius 1 cm in the transverse plane, centered on the e + e − interaction point, and must have a transverse momentum (p T ) greater than 0.1 GeV/c. Charged particles are assigned a likelihood L i , with i = µ, π, K [19], based on the range of the particle extrapolated from the CDC through the KLM; particles are identified as muons if the likelihood ratio P µ = L µ /(L µ + L π + L K ) exceeds 0.8, corresponding to a muon efficiency of about 91.5% over the polar angle range 20 • ≤ θ ≤ 155 • and the momentum range 0.7 GeV/c ≤ p ≤ 3.0 GeV/c in the laboratory frame. Electron identification uses a similar likelihood ratio P e based on CDC, ACC, and ECL information [20]. Charged particles that are not identified as muons and having a likelihood ratio P e < 0.1 are treated as pions. Calorimeter clusters not associated with reconstructed charged tracks and with energies greater than 50 MeV are classified as photon candidates. Pairs of oppositely charged tracks, of which at least one is positively identified as a muon, are selected as dimuon candidates. Pairs of oppositely charged tracks, both classified as pions, are selected as dipion candidates. Retained events contain one dimuon candidate and one dipion candidate. For η → ρ 0 γ decays, hereinafter labeled as 2π1γ, only events with at least one photon and with the photon-dipion invariant mass within 50 MeV/c 2 (±3σ) of the nominal η mass [9] are retained. Similarly, for η → π + π − η, η → γγ decay chain, hereinafter labeled as 2π2γ, only events with at least two photons having an invariant mass within 50 MeV/c 2 (±3σ) of the nominal η mass [9], and with an invariant-mass difference M (π + π − γγ) − M (γγ) within 20 MeV/c 2 (±3σ) of the nominal value are considered. In 2π1γ (2π2γ) final states, 1.2 (1.4) candidates per event are present on average, where the multiplicity is due to the photon(s). The ambiguity is resolved by choosing the one whose reconstructed η mass is closest to the nominal value. This choice has an efficiency of ∼ 90% on the MC-simulated signal samples. The where p(µµ) CM is the CM momentum of the dimuon system, is constrained to negative values for signal events, and is used to reject part of the background contribution due to QED processes (e + e − → e + e − (γ) and e + e − → µ + µ − (γ)). Further reductions of QED processes and of cosmic background events are achieved by requiring the opening angle of the charged pion candidates in the CM frame to satisfy | cos θ(ππ) CM | < 0.9.
The 2π1γ final state has contributions from dipion transitions to the Υ(1S) resonance from either Υ(2S, 3S) resonances produced in initial state radiation (ISR) events or the Υ(4S) resonance in which a random photon is incorporated into the η candidate. The high production cross section values [21] and decay rates [9] make these processes competitive with the signal transition, and particular care is needed to reduce them to negligible levels. A Boosted Decision Tree (BDT) method, as implemented in the Toolkit for Multivariate Data Analysis package [22], is trained to separate the signal events from those due to dipion transitions. The performance of the classifier is optimized and tested using MC-simulated samples for both the signal and dipion transitions. The input variables used to construct the BDT are the difference between invariant masses ∆M ππ = M (µ + µ − π + π − ) − M (µ + µ − ) and the total reconstructed mass of the event M (µ + µ + π + π − γ). The highest discrimination is provided by ∆M ππ . This variable is broadly distributed for signal events, and instead assumes the values 563.0 ± 0.4 MeV/c 2 , 894.9 ± 0.6 MeV/c 2 , and 1119.1±1.2 MeV/c 2 , for Υ(2S), Υ(3S), and Υ(4S) → π + π − Υ(1S), respectively [9], with experimental resolutions of a few MeV/c 2 . It has been verified that, with respect to a cut-based approach, the BDT method enhances the dipion rejection retaining a higher signal efficiency. The reconstructed invariant mass of the η candidate must lie within 0.93 GeV/c 2 < M (π + π − γ) < 0.98 GeV/c 2 , which retains 90% of signal events.
The overall selection efficiencies for the signal events in the 2π1γ and 2π2γ final states are = (17.64 ± 0.05)% and (5.02 ± 0.03)%, respectively, as determined from MC-simulated samples. The selection efficiency for Υ(2S, 3S, 4S) → π + π − Υ(1S) events is in the range of 10 −6 − 10 −4 , making their contribution negligible. The contributions from these and other background sources are measured with a data sample collected below the Υ(4S) resonance; a fraction of less than ∼10 −8 of the data remains in the 2π1γ final state, while no events are present in the 2π2γ final state.
The signal events are identified by the variable: where M (Υ(1S)) = M (µ + µ − ) in both final states; for the 2π1γ [2π2γ] final state, M (Υ(4S)) = M (µ + µ − π + π − γ) [M (µ + µ − π + π − γγ)] and M (η ) = M (π + π − γ) [M (π + π − γγ)]. The expected resolution for the signal is 7-8 MeV/c 2 , depending on the reconstructed η decay mode. The distribution of ∆M η versus M (η ) [M (η ) − M (η)] for the 2π1γ [2π2γ] candidates is shown in Fig. 1 [Fig. 2] in a broad range of the abscissa in order to illustrate the distribution. The signal and background yields are determined by an unbinned maximum likelihood fit to the ∆M η distribution, shown in Fig. 3. The signal component is parameterized by a Gaussian-like analytical function with mean value µ and distinct widths, σ L,R , and asymmetric-tail parameters, α L,R , either side of the peak.  between the likelihood values for a fit that includes a signal component versus a fit with only the background hypothesis. The statistical significance is estimated to be 4.2σ (4.1σ) in the 2π1γ (2π2γ) final state.
Several sources of systematic uncertainty affect the branching fraction measurement, including the number of Υ(4S) events, N Υ(4S) , (±1.4%) and the values used for the secondary branching fractions, B secondary (±2.7% for 2π1γ and ±2.6% for 2π2γ) [9]. The uncertainties in charged track reconstruction (±1.4%) and muon identification efficiency (±1.1%) are determined by comparing data and MC events using independent control samples. The largest contribution to the systematic uncertainty comes from the signal extraction procedure (±6.8% for 2π1γ and ±2.0% for 2π2γ). The uncertainty due to the choice of signal parameterizations is estimated by changing the functional forms used; the systematic uncertainty for the background form is evaluated by using secondorder polynomial or exponential functions, and by varying the range chosen for the fit. An additional uncertainty is related to the chosen values for the signal shape parameters, and is evaluated by repeating the fit while varying each of them by ±1σ with respect to its nominal value. In each case, the uncertainty is estimated as the variation in the signal yield when using an alternate configuration with respect to that obtained with the nominal one. Not all of the partial width of η → π + π − γ can be explained by a resonant decay through a ρ 0 [23], but the fractions of the nonresonant and resonant contributions are unmeasured. The potential systematic bias in the signal efficiency due to a non-null fraction of nonresonant decays is estimated by comparing the selection efficiencies between the default resonant sample and a completely nonresonant one. Half of the difference is conser- vatively assigned as systematic error (−1.9% for 2π1γ). Other possible sources of systematic uncertainties, due to discrepancies between data and MC in the efficiency of the applied selection requirements or in the photon energy calibration, have been found to be relatively small. The total systematic uncertainty is obtained by adding in quadrature all of the contributions, and amounts to 7.6% in the 2π1γ final state and 3.5% in the 2π2γ final state.
The value of the branching fraction B is calculated as: We measure B = (3.19 ± 0.96(stat.) ± 0.24(syst.)) × 10 −5 in the 2π1γ final state, and B = (4.53 ± 2.12(stat.) ± 0.16(syst.)) × 10 −5 in the 2π2γ final state. The measurements obtained from the two independent subsamples are combined in a weighted average, where the weight is the inverse of the squared sum of the statistical and systematic uncertainties on each yield, considering only the systematic contributions that are uncorrelated between the two channels. The systematic uncertainties in common between the two channels are then added in quadrature to obtain the total uncertainty. The measured branching fraction is: B(Υ(4S) → η Υ(1S)) = (3.43 ± 0.88(stat.) ± 0.21(syst.)) × 10 −5 . The statistical significance of the combined measurement is estimated by performing a simultaneous fit to the two disjoint datasets, using the same parameterizations as before, and constraining the signal normalization so that the ratio of the signal yield divided by the signal efficiency and the secondary branching fractions is the same in the two datasets. The statistical significance of the combined measurement is 5.8σ; this is reduced to 5.7σ when considering yield-related systematic uncertainties by convolving the likelihood function with a Gaussian whose width equals the systematic uncertainty. This measurement represents the first observation of the hadronic transition Υ(4S) → η Υ(1S). We also determine the ratios of branching fractions: where the decay is mediated by a hadronic state h = η or π + π − . For B(Υ(4S) → hΥ(1S)), we use the values obtained in Ref. [5], which analyzes the same data sample considered in this paper. Several systematic uncertainties cancel, being common to the numerator and denominator. The results from the two η decay modes are combined in a weighted average, as for the branching fraction measurement, and are R η /η = 0.20 ± 0.06 and R η /π + π − = 0.42 ± 0.11. The former ratio, in particular, is in agreement with the expected value in the case of an admixture of a state containing light quarks in addition to the bb pair in the Υ(4S) in bottomonium hadronic transitions [8].