Observation of and a neutral charmoniumlike structure
Using data collected with the BESIII detector operating at the Beijing Electron Positron Collider at center-of-mass energies of , 4.26, and 4.36 GeV, we observe for the first time. The Born cross sections are measured and found to be about half of those of within less than 2. In the mass spectrum, a structure at 4.02 GeV/ is found. It is most likely to be the neutral isospin partner of the observed in the process of is found. A fit to the invariant mass spectrum, with the width of the fixed to that of its charged isospin partner and possible interferences with non- amplitudes neglected, gives a mass of () MeV/ for the , where the first error is statistical and the second systematic.
pacs:14.40.Rt, 13.66.Bc, 14.40.Pq
In the study of , a distinct charged structure, , was observed in the spectrum by the BESIII ref1 () and Belle ref2 () experiments, and confirmed shortly thereafter with CLEO-c data CLEO (). A similar charged structure but with a slightly higher mass, , was soon reported in guoyp () by BESIII. As there are at least four quarks within these two charmoniumlike structures, they are interpreted as either tetraquark states, (or ) molecules, hadrocharmonia, or other configurations ref4 (). More recently, charged structures in the same mass region were observed via their decays into charmed meson pairs, including the charged in ref5 () and the charged in ref5add (). These structures together with the recently confirmed belle4430 (); belle4430conf (); lhcb4430 () and similar structures observed in the bottomonium system ref6 () indicate that a new class of hadrons has been observed. An important question is whether all these charged structures are part of isospin triplets, in which case neutral partners with should also be found. Evidence for a neutral was observed in process with CLEO-c data at center-of-mass energy (CME) =4.17 GeV CLEO (). A neutral structure, the , is expected to couple to the final state and be produced for in processes.
In this Letter, we present the first observation of at GeV, 4.26 GeV, and 4.36 GeV, and the observation of a neutral charmoniumlike structure in the spectrum. We closely follow the analysis of guoyp () with the selection of replaced with the selection of a pair of s. The data samples were collected with the BESIII detector bepc (). The CMEs and corresponding integrated luminosities are listed in Table 1.
We use a GEANT4 based geant4 () Monte Carlo (MC) simulation to optimize the event selection criteria, determine the detection efficiency, and estimate backgrounds. In the studies presented here, the is reconstructed via its electric-dipole (E1) transition with , where denotes 16 hadronic final states: , , , , , , , , , , , , , , , and . The initial state radiation (ISR) is simulated with KKMC KKMC (), where the Born cross section of is assumed to follow the line-shape guoyp ().
The selection of charged tracks, photons, and candidates are described in Refs. ref13 (); guoyp (). A candidate is reconstructed from a pair of photons with an invariant mass in the range 15 MeV/ (15 MeV/), where is the nominal mass ref14 (). The event candidates of , are required to have at least one combination with the mass recoiling against , , in the mass region ( GeV/) and with the mass recoiling against , , in the mass region ( GeV/).
To determine the species of final state particles and to select the best photon candidates when additional photons (and or candidates) are found in an event, the combination with the minimum value of is selected for further analysis. Here is the of the initial-final four-momentum conservation () kinematic fit, is the of particle identification (PID) of each charged track using the energy loss in the main drift chamber and the time measured with the time-of-flight system, is the number of the charged tracks, and is the sum of the s of the s and in each final state with the invariant mass of the daughter photon pair constrained to that of the parent. There is also a requirement, which is optimized by maximizing the figure of merit , where and are the numbers of Monte Carlo (MC) simulated signal and background events, respectively. The requirement has an efficiency of 82% for decays with only charged or particles in the final states, while the requirement has an efficiency of 81% for the other decays corr (). A similar optimization is performed to determine the candidate mass window around its nominal value, which is found to be MeV/. This mass window contains 77% of decays with only charged or particles in final states and 74% for the other decays.
The inset of Fig. 1 shows the scatter plot of , which corresponds to the invariant mass of the reconstructed candidate, versus , which corresponds to the invariant mass of the reconstructed candidate, summed over the events at , 4.26, and 4.36 GeV, where a clear cluster of events corresponding to the signal is observed. Figure 1 shows the projection of the invariant mass distribution of candidates for events in the signal region ( GeV/ ), where a clear peak at the mass is observed. The events in the sideband regions, 2.865 GeV/c 2.900 GeV/c and 3.050 GeV/c 3.085 GeV/c are used to study the background. To extract the number of signal events, the mass spectrum is fitted with a MC simulated signal shape convolved with a Gaussian function to represent the data-MC mass resolution difference, together with a linear background term. A simultaneous fit to the mass spectrum summed over the 16 decay modes at the three CME points yields the numbers of signal events () listed in Table 1. Figure 1 also shows the fit results summed over the three CME points.
The Born cross section is calculated with the formula
where is the number of observed signal events; is the integrated luminosity; is the initial radiative correction factor, which is taken to be the same as that for the analysis of guoyp (); is the vacuum polarization factor vacu (); is the detection efficiency for the decay mode in the decay without consideration of any possible intermediate structures and with ISR and vacuum polarization effects considered in the MC simulation; is the corresponding branching fraction; is the branching fraction of .
The measured Born cross sections are listed in Table 1. The ratios of the Born cross sections for the neutral and charged modes are also listed in Table 1; the cross sections for the charged channel are taken from Ref. guoyp (), where vacuum polarization effects were not taken into account. A corresponding correction factor is applied to the previous Born cross section. The common systematic uncertainties in the two measurements cancel in the ratio calculation. The combined ratio is obtained with a weighted least squares method xx () and determined to be , which is within 2 of the expectation of isospin symmetry, 0.5.
Systematic uncertainties in the cross section measurement mainly come from the luminosity measurement (), branching fraction of , branching fractions of , detection efficiencies (), radiative correction factors (), vacuum polarization factors () vacu (), and fits to the mass spectrum. The integrated luminosity at each CME points is measured using large-angle Bhabha events and has an estimated uncertainty of 1.0%. The and branching fractions are taken from Refs. ref11 (); ref13 (), and the uncertainties in the radiative correction are the same as those used in the analysis of guoyp (). The uncertainties in the vacuum polarization factor are 0.5% vacu (). The detection efficiency uncertainty estimates are done with the same way as described in Refs. ref13 (); ref16 (). The uncertainty due to the mass () is estimated by changing its mass by 1 of its world average value ref14 (); the uncertainties due to the background shapes () are estimated by changing the background function from a first-order to a second-order polynomial; the uncertainty from the mass resolution () is estimated by varying the mass resolution difference between data and MC simulation by one standard deviation; the uncertainty from fit range () is estimated by extending the fit range; the uncertainty from the substructure () is estimated by considering the efficiency with and without the inclusion of a . The contribution from each source of systematic error are listed in Table 2.
Assuming all of the above uncertainties are independent, the total systematic uncertainties in the cross section measurements are determined to be between 10% and 13%. The uncertainty in , not listed in Table 2 but common to all CME points, is 15.7% ref14 () and is quoted separately in the cross section measurement.
Intermediate states are studied by examining the distribution (which corresponds to the reconstructed invariant mass) for the selected candidate events. The signal events are selected by requiring in the range of [3.51, 3.55], and events in the sideband regions [3.45, 3.49] and [3.57, 3.61] are used to study the background. From the two combinations of the recoil mass in each event, we retain the one with the larger recoil mass value, and denote this as . Figure 2 shows the distribution for the signal events where there is an obvious peak near 4.02 GeV/, which corresponds to the expected position of a signal.
An unbinned maximum likelihood fit is applied to the distribution summed over all 16 decay modes. The data at , 4.26, and 4.36 GeV are fitted simultaneously with the same signal function with common mass and width. The signal shape is parametrized with a constant-width relativistic Breit-Wigner function convolved with a Gaussian-distributed mass resolution, where the mass resolution is determined from a fit to a MC sample with the width set to zero. Because of the limited statistics of the signal, its width is fixed to that of its charged partner, () MeV guoyp (). Assuming the spin and parity of the are , a phase space factor is included in the partial width, where is the momentum in the rest frame and is the momentum in the rest frame.
There are two types of backgrounds in the distribution. One is the non- background in the signal region, which can be represented by the sideband events, and the other is the non- events that may come from three-body decays or from production of intermediate scalar states, such as the , that decay into . Since the widths of the low-mass scalar particles are large, these non- events can be reasonably well described with a phase space distribution. For the non- background, a comparison of the sideband events with the simulated phase space events indicates that it can also be described with a three-body phase space distribution. Thus, in the fit all of the background sources are described with a single MC-simulated phase space shape with a total normalization that is left as a free parameter. In the fit, the signal shape mentioned above is multiplied by the efficiency, which depends on . Interference between the signal and background is neglected.
The solid curve in Fig. 2 shows the fit results, which yields a mass of MeV/. The mass difference between neutral and charged is (stat.) MeV/, which agrees with zero within error. By projecting the events into a histogram with 50 bins, the goodness of the fit is calculated from the combined values, the number of bins and the number of free parameters at three CME points, and found to be . Here the event number in each bin used in the evaluation is required to be larger than 7. The statistical significance of the signal is determined from a comparison of the fit likelihoods with and without the signal. Additional fit are also performed with different signal shapes, and background shapes. In all cases, the minimum significance is found to be above . The numbers of signal events are listed in Table 3.
The Born cross section is calculated with eq. 1, with the measured numbers of observed signal and MC-determined detection efficiencies for the channel.
The systematic uncertainties on the mass come from uncertainties in the mass calibration and energy scale, parametrizations of the signal and background shapes, mass dependence of the efficiency, width assumption, MC modeling with a different value, and mass resolution. The uncertainty from the mass calibration is estimated by using the difference, MeV/c, between the measured and known mass. The uncertainty from the photon energy scale is estimated with for photons with low energy, and with radiative Bhabha processes for photons with high energy ref11 (). After adjusting the MC energy scale accordingly, the resulting changes in the mass of are negligible. The value of is uncertain; two possible alternatives, and , are used to estimate the corresponding systematic errors. A difference of 0.4 MeV/ in the mass is found under different assumptions. The uncertainty due to the background shape is determined by changing the phase space shape to a parametrized background function, . Here is mass of the background, and are the two extreme points determined by the minimal and maximal mass. for or . The coefficients and are determined by the fit ref5add (). A difference of 0.1 MeV/ is found and taken as the systematic uncertainty. The uncertainty due to the mass dependence of the efficiency is determined by assuming a uniform efficiency in the whole recoil mass region, and the difference is found to be negligible. The uncertainty due to the mass resolution is estimated by varying the data-MC difference in resolution by one standard deviation of the measured uncertainty in the mass resolution of the signal; the difference in the mass is negligible. Similarly, the uncertainty due to the fixed width is estimated by varying the width determined for its charged partner by one standard deviation. The difference is 0.1 MeV/ and is taken as the systematic error. Assuming all the sources of the systematic uncertainty are independent, the total systematic error is estimated to be 3.8 MeV/.
The systematic uncertainties in the measured Born cross section, , are estimated in the same way as for . In addition to those common parts in the measurement, the uncertainties due to signal parametrization (), background shape (), signal window selection (), mass resolution (), efficiency (), and MC model () are considered; their values are summarized in Table 4.
The ratios of Born cross section for between neutral and charged modes at three center-of-mass energies are listed in Table 3. Similar to the calculation of the ratio, the same correction factor is also applied to the previously measured Born cross section. The common systematic uncertainty between neutral and charged mode cancel. The combined ratio is determined to be with the same method as for the combined , which is well within 1 of the expectation of isospin symmetry, 1.0.
In summary, we observe at , 4.26, and 4.36 GeV for the first time. The measured Born cross sections are about half of those for , and agree with expectations based on isospin symmetry within systematic uncertainties. A narrow structure with a mass of MeV/ is observed in the mass spectrum. This structure is most likely the neutral isospin partner of the charged observed in the process guoyp (). This observations indicate that there is no anomalously large isospin violations in and system.
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; Joint Funds of the National Natural Science Foundation of China under Contracts Nos. 11079008, 11179007, U1232201, U1332201; National Natural Science Foundation of China (NSFC) under Contracts Nos. 10935007, 11121092, 11125525, 11235011, 11079023, 11322544, 11335008; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS under Contracts Nos. KJCX2-YW-N29, KJCX2-YW-N45; 100 Talents Program of CAS; German Research Foundation DFG under Contract No. Collaborative Research Center CRC-1044; Istituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under Contract No. DPT2006K-120470; Russian Foundation for Basic Research under Contract No. 14-07-91152; U. S. Department of Energy under Contracts Nos. DE-FG02-04ER41291, DE-FG02-05ER41374, DE-FG02-94ER40823, DESC0010118; U.S. National Science Foundation; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.
- (1) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 110, 252001 (2013).
- (2) Z. Q. Liu et al. (Belle Collaboration), Phys. Rev. Lett. 110, 252002 (2013).
- (3) T. Xiao, S. Dobbs, A. Tomaradze and K. K. Seth, Phys. Lett. B 727, 366 (2013).
- (4) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 111, 242001 (2013).
- (5) J. Z. Bai et al. (BES Collaboration), Nucl. Instrum. Meth. A 344, 319 (1994); Nucl. Instrum. Meth. A 458, 627 (2001).
- (6) S. Agostinelli et al. (GEANT4 Collaboration), Nucl. Instrum. Meth. A 506, 250 (2003).
- (7) S. Jadach, B.F.L. Ward and Z. Was, Comput. Phys. Commun. 130, 260 (2000); Phys. Rev. D 63, 113009 (2001).
- (8) Q. Wang, C. Hanhart, and Q. Zhao, Phys. Rev. Lett. 111, 132003 (2013); F.-K. Guo, C. Hidalgo-Duque, J. Nieves, and M. PavonValderrama, Phys. Rev. D 88, 054007 (2013); G. Li, Eur. Phys. J. C 73, 2621 (2013); C.-Y. Cui, Y.-L. Liu, W.-B. Chen, and M.-Q. Huang, Eur. Phys. J. C 73, 12 (2013); J.-R. Zhang, Phys. Rev. D 87, 116004 (2013); J.M. Dias, F. S. Navarra, M. Nielsen, and C. M. Zanetti, Phys. Rev. D 88, 016004 (2013); M.B. Voloshin, Phys. Rev. D 87, 091501 (2013); E. Braaten, Phys. Rev. Lett. 111, 162003 (2013); E. Wilbring, H.W. Hammer, and U. G. Meißner, Phys. Lett. B 726, 326 (2013); D.-Y. Chen, X. Liu, and T. Matsuki, Phys. Rev. D