First observation of the P-wave spin-singlet bottomonium states and
We report the first observation of the spin-singlet bottomonium states and produced in the reaction using a data sample collected at energies near the resonance with the Belle detector at the KEKB asymmetric-energy collider. We determine and , which correspond to -wave hyperfine splittings and , respectively. The and are observed with significances of and , respectively. We also report measurements of the cross sections for relative to that for .
pacs:14.40.Pq, 13.25.Gv, 12.39.Pn
The Belle Collaboration
Bottomonium is the bound system of quarks and is considered an excellent laboratory to study Quantum Chromodynamics (QCD) at low energies. The system is approximately non-relativistic due to the large quark mass, and therefore the quark-antiquark QCD potential can be investigated via spectroscopy QWG ().
The spin-singlet states and alone provide information concerning the spin-spin (or hyperfine) interaction in bottomonium. Measurements of the masses provide unique access to the -wave hyperfine splitting, , the difference between the spin-weighted average mass of the -wave triplet states ( or ) and that of the corresponding , or . These splittings are predicted to be close to zero godros (), and recent measurements of the mass correspond to a -wave hyperfine splitting that validates this expectation for the 1P level in charmonium: hcmass ().
Recently, the CLEO Collaboration observed the process at a rate comparable to that for in data taken above open charm threshold cleo_hcpipi (). Such a large rate was unexpected because the production of requires a -quark spin-flip, while production of does not. Similarly, the Belle Collaboration observed anomalously high rates for () at energies near the mass 5s_rate (). Together, these observations motivate a search for above open-bottom threshold at the resonance.
In this Letter, we report the first observation of the and produced via in the region. We use a data sample collected near the peak of the resonance () with the Belle detector BELLE_DETECTOR () at the KEKB asymmetric-energy collider KEKB ().
We observe the states in the missing mass spectrum of hadronic events. The missing mass is defined as where is the 4-momentum of the determined from the beam momenta and is the 4-momentum of the system. The transitions between states provide high-statistics reference signals.
Our hadronic event selection requires a reconstructed primary vertex consistent with the run-averaged interaction point (IP), at least three high-quality charged tracks, a total visible energy greater than , a total neutral energy of , more than one large-angle cluster in the electromagnetic calorimeter and that the total center-of-mass momentum have longitudinal component smaller than hadronbj (). The candidates are pairs of well reconstructed, oppositely charged tracks that are identified as pions and do not satisfy electron-identification criteria. Continuum () background is suppressed by requiring the ratio of the second to zeroth Fox-Wolfram moments to satisfy Fox-Wolfram (). The resulting spectrum, which is dominated by combinatoric pairs, is shown in Fig. 1.
Prior to fitting the inclusive spectrum we study reference channels and peaking backgrounds arising from transitions between states. A high purity sample of such transitions is obtained by reconstructing pairs in the event in addition to the pair. For these studies the hadronic event selection criteria are not applied, while for the pair we use the same selection as was employed in Ref. 5s_rate (). MC studies indicate that the shape of the peaks in is independent of whether the are reconstructed in the hadronic environment or in this much cleaner environment. In addition, to suppress radiative Bhabha events in which the photon converts, producing a fake , we require that the opening angle between the candidate pions in the laboratory frame satisfies . In Fig. 2 (a) we present the two-dimensional distribution of mass vs. for events satisfying these criteria.
Clear peaks are visible along a diagonal band, where is roughly equal to , and correspond to fully reconstructed events. Also along the diagonal is a diffuse background of events that arise due to the process , where the conversion pair is reconstructed as , or from non-resonant events. Events from the band satisfying are projected onto the axis and fitted to the sum of a linear background and a Gaussian joined to a power-law tail on the high mass side. The high-side tail is due to Initial State Radiation (ISR) photons. This latter function is analogous to the well-known Crystal Ball function skwarthesis () but has the tail on the higher rather than lower side. We thus refer to it as a ’reversed Crystal Ball’ (rCB) function. The fitted spectra from this band are shown in Figs. 2 (b)-(d), and the resulting yields, masses and width of the rCB function for the states are displayed in Table 1. The masses obtained are consistent with the world average values PDG ().
The structures in the horizontal band in Fig. 2 (a), where is roughly equal to , arise from events in which a daughter in the event decays to . In Figs. 2 (e)-(f) we present projections from this band, subject to the requirement . The peaks at the and masses arise from events having transitions to or , followed by inclusive production of , and are fitted to rCB functions. Peaks at and arise from events in which a or is produced inclusively in decays or via ISR, and then decays to , and are fitted to single and double Gaussians, respectively.
The threshold for inclusive production results in a sharp rise in the spectrum, due to , very close to the mass of . Rather than veto combinations with invariant masses near , which significantly distorts the spectrum in the vicinity, we obtain the contamination by fitting the invariant mass corresponding to bins of .
The spectrum is divided into three adjacent regions with boundaries at , , and and fitted separately in each region. In the first two regions, we use a 6th-order Chebyshev polynomial, while in the third we use a 7th-order one. In the third region, prior to fitting, we subtract the contribution due to bin-by-bin. The signal component of the fit includes all signals seen in the data as well as those arising from transitions to and . We fit these additional signals using the tail parameters of the and fixed widths found by linear interpolation in mass from the widths of the exclusively-reconstructed peaks. The peak positions of all signals are floated, except that for , which is poorly constrained by the fit. The confidence levels of the fits in the three regions are , and , respectively.
We studied several sources of systematic uncertainty. The background polynomial order was increased by three, and the range of the fits performed were altered by up to 100 . Different signal functions were used, including symmetric Gaussians and rCB functions with the width parameters left free. We altered our selection criteria: tightening the requirements on the proximity of track origin to the IP, increasing the minimum number of tracks to four, and imposing the requirement used in the study. In Table 3 a summary of our systematic studies is presented.
The values in the table represent the maximal change of parameters under the variations explored. We estimate an additional uncertainty in mass measurements based on the differences between the observed values of the fitted peak positions and their world averages. The total systematic uncertainties presented in Table 2 represent the sum in quadrature of all the contributions listed in Table 3. The signal for the is marginal and therefore systematic uncertainties on its related measurements are not listed in the table. The significances of the and signals, with systematic uncertainties accounted for, are and , respectively.
The measured masses of and are and , respectively. Using the world average masses of the states, we determine the hyperfine splittings to be and , respectively, where statistical and systematic uncertainties are combined in quadrature.
We also measure the ratio of cross sections for to that for . To determine the reconstruction efficiency we use the results of resonant structure studies reported in Ref. belle_zb () that revealed the existence of two charged bottmonium-like states, and , through which the transitions we are studying primarily proceed. These studies indicate that the most likely have , and therefore in our simulations the transitions are generated accordingly. To estimate the systematic uncertainty in our reconstruction efficiencies, we use MC samples generated with all allowed quantum numbers with .
We find that the reconstruction efficiency for the is about 57%, and that those for the and relative to that for the are and , respectively. The efficiency of the requirement is estimated from data by measuring signal yields with . For , and we find , and , respectively. From the yields and efficiencies described above, we determine the ratio of cross sections to be for the and for the . Hence and proceed at similar rates, despite the fact that the production of requires a spin-flip of a -quark.
The rate of is much larger than the upper limit for that of obtained by the BaBarCollaboration hb_pipi_babar (). This is consistent with the observation that the rates for with are much larger than those for for 5s_rate (). The only previous evidence for the is a excess in at presented by BaBar hb_babar ().
We have also used of collisions at the resonance to search for ( is kinematically forbidden). The overall efficiency, assuming the efficiency at to be the same as that at , is relative to that for . From our observed yield of , we therefore set an upper limit on the ratio of at the to that at the of at 90% C.L.
In summary, we have observed the -wave spin-singlet bottomonium states and in the reaction . The masses correspond to hyperfine splittings that are consistent with zero. We also have observed that the cross sections for these processes and that for are of comparable magnitude, indicating the production of at the resonance must occur via a process that avoids the expected suppression related to heavy quark spin-flip.
We thank the KEKB group for excellent operation of the accelerator, the KEK cryogenics group for efficient solenoid operations, and the KEK computer group and the NII for valuable computing and SINET4 network support. We acknowledge support from MEXT, JSPS and Nagoya’s TLPRC (Japan); ARC and DIISR (Australia); NSFC (China); MSMT (Czechia); DST (India); MEST, NRF, NSDC of KISTI, and WCU (Korea); MNiSW (Poland); MES and RFAAE (Russia); ARRS (Slovenia); SNSF (Switzerland); NSC and MOE (Taiwan); and DOE and NSF (USA).
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