In the bottomonium sector, the hindered magnetic dipole transitions between P-wave states h b ð2PÞ → χ bJ ð1PÞγ, J ¼ 0, 1, 2, are expected to be severely suppressed according to the relativized quark model, due to the spin flip of the b quark. Nevertheless, a recent model following the coupled-channel approach predicts the corresponding branching fractions to be enhanced by orders of magnitude. In this Letter, we report the first search for such transitions. We find no significant signals and set upper limits at 90% confidence level on the corresponding branching fractions: B½h b ð2PÞ → γχ b0 ð1PÞ < 2.7 × 10 -1 , B½h b ð2PÞ → γχ b1 ð1PÞ < 5.4 × 10 -3 and B½h b ð2PÞ → γχ b2 ð1PÞ < 1.3 × 10 -2 . These values help to constrain the parameters of the coupled-channel models. The results are obtained using a 121.4 fb -1 data sample taken around ffiffi ffi s p ¼ 10.860 GeV with the Belle detector at the KEKB asymmetric-energy e þ e -collider. DOI: 10.1103/PhysRevD.111.L011102

In recent years, bottomonium spectroscopy has shown a number of unexpected results. A key one among them is the observation of the spin-singlet P-wave state h b ð2PÞ by the Belle Collaboration [1]. The production of spin-singlet bottomonia is generally rare in e þ e -collisions because it requires the spin flip of a heavy quark in a hadronic or radiative transition. Nevertheless, h b ð2PÞ is produced via the ϒð10860Þ → h b ð2PÞπ þ π -transition with a surprisingly large rate. The observation of this unexpected enhancement has led to the discovery of the exotic four-quark states Z b ð10610Þ AE and Z b ð10650Þ AE [2] that are produced as intermediate states in the di-pion transitions.

In this analysis, we search for the hindered magnetic dipole (M1) transitions between the spin-singlet and spintriplet states h b ð2PÞ → γχ bJ ð1PÞ. This is the first search for such kind of transitions. According to the relativized quark model [3], these are expected to be severely suppressed because of the heavy quark spin flip, and branching fractions of order 10 -6 -10 -5 are predicted. Nevertheless, a recent study [4] considering coupled-channel effects giving rise to B meson loop diagrams predicts the branching fractions for the considered transitions to be in the order of 10 -2 -10 -1 . The isospin violating ϒð3SÞ → π 0 h b ð1PÞ decay channel with a subsequent electric dipole transition to the η b ð1SÞ found by the BABAR Collaboration [5] has the same final states, γγh b , as the one in the electromagnetic cascades ϒð3SÞ → γχ bJ ð2PÞ (J ¼ 0, 1, 2) and χ bJ ð2PÞ → γh b ð1PÞ [4]. Results for the hindered M1 transitions involving the h b are lacking. Therefore, experimental results are needed for a correct understanding of the transitions. Many recent results in the quarkonium sector show that transitions which were once unlikely to observe are now accessible. We are thus further motivated to search for the hindered M1 transitions between P-wave bottomonia for the first time.

The analysis setup is fully exclusive. We reconstruct the di-pion transition from ϒð10860Þ in order to tag the h b ð2PÞ production. The χ bJ ð1PÞ have large radiative decay to the ϒð1SÞ, which can subsequently decay to μ þ μ -. The radiative decays χ bJ ð1PÞ → γϒð1SÞ are thus chosen to tag the final state of the M1 transition, so that there are two photons in the cascade. Therefore, we reconstruct the complete decay chain

We label as γ 1 the photon radiated in the h b ð2PÞ → γχ bJ ð1PÞ decay, and γ 2 the photon emitted in χ bJ ð1PÞ → γϒð1SÞ decays.

We use a 121.4 fb -1 data sample collected at the ϒð10860Þ resonance by the Belle detector [6,7] at the KEKB asymmetric-energy e þ e -collider [8,9]. The average center-of-mass (c.m.) energy of this 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 (ACCs), a barrellike arrangement of time-of-flight scintillation counters, and an electromagnetic calorimeter composed of CsI(Tl) crystals (ECL) located inside a superconducting solenoid coil that provided a 1.5 T magnetic field. An iron fluxreturn yoke located outside of the coil (KLM) was instrumented with resistive-plate chambers to detect K 0 L mesons and muons.

For the Monte Carlo (MC) simulation, we use the EVTGEN generator [10]. Following the results presented in Ref. [1], the ϒð10860Þ → h b ð2PÞπ þ π -transition is simulated assuming it proceeds exclusively through the intermediate Z b ð10610; 10650Þ AE states. Each angular distribution in the signal decay chain is generated according to the corresponding spin dynamics. Final-state radiation is included using the PHOTOS package [11]. Background MC samples include the production of B þ , B 0 , and B 0 s mesons; the continuum processes e þ e -→ q q, q ¼ u, d, s, c; and two-photon interactions. The detector response is modeled using GEANT3 [12]. Simulation takes into account temporal variations of the detector configuration and data-taking conditions.

Selection requirements are optimized using the figure of merit, FOM ¼ S ffiffiffiffiffiffiffi SþB p

, where the number of signal (S) and background (B) events are determined from simulation. The B½h b ð2PÞ → γχ bJ ð1PÞ values are assumed to be 1.4%, 4.0%, and 5.0% for J ¼ 0, 1, and 2, respectively [4]. The selection requirements are summarized in Table I. Charged tracks must have transverse momentum above 50 MeV=c and originate from a cylindrical region of length 6.0 cm along the beam axis and radius 1.0 cm in the transverse plane, centered on the e þ e -interaction point. Moreover, we only retain tracks that are in the CDC geometric acceptance and are associated with more than 20 hits in this subdetector. We select events with exactly four tracks. Muon candidates are identified by requiring P μ ¼ L μ L μ þL π þL K > 0.8, where the likelihood L i ; i ¼ μ, π, K, is assigned based on the range of the charged particle extrapolated from the CDC through KLM and on deviation of hits from the extrapolated track [13]. For pion candidates, we apply an electron veto P e < 0.4, where P e is a similar likelihood ratio based on CDC, ACC, and ECL information [14]. To suppress the residual background from photon conversion, we apply a requirement on the opening angle between the pions in the laboratory frame, α ππ > 11.7°. We apply a requirement on the μ þ μ -mass, 9.0 < M μμ < 9.8 GeV=c 2 , which retains 96% of the signal events.

Photons are detected as ECL clusters without associated charged particles. We require the energies of the γ 1 and γ 2 candidates in the laboratory frame to exceed 267 and 305 MeV, respectively. We veto the π 0 background, mostly given by the process ϒð10860Þ → ϒð2SÞπ 0 π 0 , by discarding events with one or more candidates for which the diphoton invariant mass Mðγ 1 γ 2 Þ lies in a region of 20 MeV around the known π 0 mass. Similarly, we veto the η → γγ decay requiring jMðγ 1 γ 2 Þ -mðηÞj > 33.4 MeV=c 2 to suppress the background coming from h b ð2PÞ → η½γγϒð1SÞ½μ þ μ -. Finally, we perform a 4C kinematic fit [15], constraining the total four-momentum of the final-state particles to the four-momentum of the initial state and requiring corresponding p-value to exceed 10 -5 . If multiple candidates are found, the one with the highest p-value is chosen. The signal region is defined as 10.239

The efficiencies of the selection requirements, summarized in Table I, are 5.2%, 10.9%, 10.7% for the J ¼ 0, 1, 2

TABLE I. Summary of the applied selection criteria. Variable Value M μμ ½9.0; 9.8 GeV=c 2 p T ðπÞ >50 MeV=c Eðγ

½315; 436 MeV=c 2 channels, respectively. Figure 1 shows the 2D distribution of simulated events and the signal region. We observe a few background events in the simulated sample. A majority of them comes from the process e þ e -→ π þ π -π 0 χ b1 ð1PÞ, where the three pions are produced either directly or by the decay of an intermediate ω meson. This background, with an expected yield of 0.92 events, is irreducible, but the corresponding branching fraction has been measured [16] and can be used to estimate the expected number of events from simulation. Another source of background is e þ e -→ μ þ μ -3γ, where one of the photons is converted in the detector. This sample yields 0.1 events. The last source of background is h b ð2PÞ → η½γγϒð1SÞ½μ þ μ -with branching fraction ð7.1 3.7 3.2 AE 0.8Þ × 10 -3 [17], which is reconstructed with 0.05% efficiency after applying the η → γγ veto. From this source we retain 0.02 events.

The two-dimensional distribution in

, which is currently under study at Belle. In the signal region, the observed count is zero on experimental data, while the background count is 1.04 in simulation.

The expected number of background events is a key input for the estimation of the upper limits on the signal branching fractions. The correction factor and systematic uncertainty on the background counts are extracted from the data/MC comparison in the M rec ðπ þ π -Þ sidebands. This comparison is done after applying a looser selection in order to increase statistics in the sidebands. With this selection we drop the 4C kinematic fit and lower the photon energy requirement to 150 MeV for both γ 1 and γ 2 . We define the three sidebands [10.000, 10.130], [10.185, 10.239], ½10.280; 10.500 GeV=c 2 . In the combined sidebands we measure 1466 þ39 -38 counts on data and 1444 AE 45 on simulation. The definition of the sidebands and the measured number of events, alongside with the data/MC ratios, are reported in Table II. Based on the results from the combined sidebands, we find that the simulation correctly describes the background within a AE4% systematic uncertainty. The expected number of background events in the signal region is 1.06 þ0.29 -0.20 , where the uncertainty is both due to the correction factor and limited statistics in the simulated sample.

In order to validate the analysis procedure and to estimate the systematic uncertainty in the efficiency, we apply a similar selection to a different dataset taken at the ϒð3SÞ resonance. The dataset corresponds to 2.9 fb -1 taken at the resonance peak plus 0.3 fb -1 taken in an off-resonance scan. We reconstruct the cascade decays FIG. 1. Two-dimensional distribution of the simulated events. The signal region is the rectangle defined by the conditions 10.239

FIG. 2. Two-dimensional distribution of experimental data and expected background. The red dashed rectangle defines the signal region. The blue dashed lines enclose the blind region 10.130 < M rec ðπ þ π -Þ < 10.185 GeV=c 2 where the decay ϒð10860Þ → π þ π -ϒ J ð1DÞ → π þ π -γγϒð1SÞ may be observed.

TABLE II. Counted number of events in the sidebands of the M rec ðπ þ π -Þ variable. The uncertainties include systematic contributions and are propagated by summing in quadrature. Sideband (GeV) MC Data Data=MC [10.000, 10.130] 404 þ12 -11 390 þ21 -20 0.97 AE 0.06 [10.185, 10.239] 98 AE 12 124 þ12 -11 1.26 þ0.20 -0.19 [10.280, 10.500] 942 AE 25 952 þ32 -31 1.01 AE 0.04 All 1444 AE 45 1466 þ39 -38 1.02 AE 0.04

Concerning the topology, the main difference with respect to the signal channels is that the radiated photons are softer, however their energy is of the same order of magnitude (∼100 MeV). The di-pion transition ϒð2SÞ → π þ π -ϒð1SÞ ensures that pions have low momentum as for the signal cascade. We apply slightly different photon energy requirements than those described in Table I. The photon energy in the lab frame is required to be higher than 60 MeV. Photons with 80 < E c:m: < 150 MeV are selected to reconstruct the ϒð3SÞ → γχ bJ ð2PÞ decays, while photons with 160 < E c:m: < 280 MeV are associated with the χ bJ ð2PÞ → γϒð2SÞ processes. A stringent requirement 9.770 < M rec ðπ þ π -Þ < 9.810 GeV=c 2 is applied as for the signal channel. The π 0 → γγ is vetoed analogously to the signal selection, while the veto for η → γγ is not applied. Due to the presence of multiple candidates, we perform a 4C kinematic fit and select the one with highest p-value.

In Fig. 3 we show the data/MC comparison on the Mðμμππγ 2 Þ -MðμμÞ variable, where γ 2 is the photon radiated by the χ bJ ð2PÞ states. The two distributions are background-free and agree well. We count the number of events in the region 700 < Mðμμππγ 2 Þ -MðμμÞ < 850 MeV=c 2 . We measure N Data ¼ 211 þ15 -14 , N MC ¼ 209 AE 24, N Data =N MC ¼ 1.01 AE 0.14. The uncertainty on N MC includes systematic contributions from known branching fractions. Thus, we estimate an overall 14% uncertainty on the efficiency estimation due to event selection.

All the sources of systematic uncertainty and their values are summarized in Table III.

We estimate the upper limits on the signal branching fractions by generating pseudoexperiments and applying the Feldman-Cousins method [18] for the construction of the confidence belts. The number of pseudoevents in the Mðμμγ 1 γ 2 Þ -Mðμμγ 2 Þ variable for each channel h b ð2PÞ → γχ bJ ð1PÞ, J ¼ 0, 1, 2, is extracted from a Poisson distribution with mean defined as

→ γϒð1SÞ × B½ϒð1SÞ → μμ [20], ε J is the selection efficiency, and B sig ðJÞ ¼ B½h b ð2PÞ → γχ bJ ð1PÞ. In order to include systematic uncertainties in the upper limit estimation, all the quantities except B sig ðJÞ are sampled from a Gaussian distribution with mean equal to the expected value and standard deviation equal to its uncertainty. The mean number of background events is ν b ¼ N b sf, where N b is sampled from a Poisson distribution with mean equal to the unweighted MC counts, s is the mean weight, and f is the correction factor, sampled from a Gaussian distribution with mean 1.02 and standard deviation 0.04 (see Table II).

The upper limits at 90% confidence level (CL) are estimated by using the Feldman-Cousins method, where the theoretical Poisson distribution is replaced by the distribution of counts generated in the pseudoexperiments. The results for the investigated channels are summarized in Table IV. TABLE III. Summary of the systematic uncertainties contributing to the observed upper limits of the signal branching fractions. Source Uncertainty Luminosity AE1.70 fb -1 σðe þ e -→ h b ð2PÞπ þ π -Þ AE360 fb B½χ b0 ð1PÞ → γϒð1SÞ AE0.27 × 10 -2 B½χ b1 ð1PÞ → γϒð1SÞ AE2.0 × 10 -2 B½χ b2 ð1PÞ → γϒð1SÞ AE1.0 × 10 -2 B½ϒð1SÞ → μ þ μ - AE0.05 × 10 -2 Efficiency h b ð2PÞ → γχ b2 ð1PÞ AE1.50 × 10 -2 h b ð2PÞ → γχ b1 ð1PÞ AE1.53 × 10 -2 h b ð2PÞ → γχ b0 ð1PÞ AE7.28 × 10 -3 Background counts AE4.24 × 10 -2

TABLE IV. Observed upper limits at 90% CL for the branching fractions of the investigated transitions. Channel B h b ð2PÞ → γχ b2 ð1PÞ <1.3 × 10 -2 h b ð2PÞ → γχ b1 ð1PÞ <5.4 × 10 -3 h b ð2PÞ → γχ b0 ð1PÞ <2.7 × 10 -1

In conclusion, we performed the first search for hindered M1 transitions between P-wave states of the bottomonium system. Using the Belle data sample of 121. The upper limits are consistent with the relativized quark model expectations [3] and help to constrain parameters of the coupled-channel model [4].