Evidence of a new narrow resonance decaying to
We report measurements of and decays using events collected at the resonance with the Belle detector at the KEKB asymmetric-energy collider. Evidence of a new resonance in the final state is found with a statistical significance of . This state has a mass of MeV/, a value that is consistent with theoretical expectations for the previously unseen meson. We find no other narrow resonance and set upper limits on the branching fractions of the and decays.
pacs:13.25.Hw, 13.20.Gd, 14.40.Pq
The Belle Collaboration
During the last decade, a number of new charmonium ()-like states were observed, many of which are candidates for exotic states brambilla (). The first of these, the , has been observed by six different experiments in the same final state belle1 (); cdf1 (); do1 (); babar1 (); lhcb (); cms (). A recent update from Belle belle_recent () and LHCb lhcb () results in a world average mass at MeV pdg () and a stringent upper bound on its width ( MeV) belle_recent (). The proximity of its mass to the threshold makes it a good candidate for a molecule swanson (). Other alternative models have been proposed, such as a tetraquark Lmaiani () or a hybrid meson Lihybrid ().
Radiative decays can illuminate clearly the nature of hadrons. For example, the observation of confirmed the -even parity assignment for the babarprl102 (); belle3 (). The and decays are forbidden by -parity conservation in electromagnetic processes. However, if the is a tetraquark or a molecular state, it may have a -odd partner, which could decay into and final states terasaki (); nieves ().
In the charmonium family, the observation of a -wave meson and its decay modes would test phenomenological models cornell (); buchmuller (). The as-yet undiscovered ) and states are expected to have significant branching fractions to and , respectively estia2002 (); cho1994 (). -wave states and their properties were predicted long ago but remain unconfirmed estia2002 (); cho1994 (). The E705 experiment reported an indication of a state in anything, with a mass of MeV e705 (); however, the statistical significance of this result was below the threshold for evidence.
In this letter, we report measurements of and decays, where the and decay to mixchg (). These results are obtained from a data sample of events collected with the Belle detector abashian () at the KEKB asymmetric-energy collider operating at the resonance kurokawa ().
The meson is reconstructed via its decays to ( or ). To reduce the radiative tail in the mode, the four-momenta of all photons within 50 mrad with respect to the original direction of the or tracks are included in the invariant mass calculation, hereinafter denoted as . The reconstructed invariant mass of the candidates is required to satisfy 2.95 GeV GeV or 3.03 GeV GeV. For the selected candidates, a vertex-constrained fit is applied and then a mass-constrained fit is performed in order to improve the momentum resolution. The and candidates are reconstructed by combining candidates with a photon having energy () larger than 200 MeV in the laboratory frame. Photons are reconstructed from energy depositions in the electromagnetic calorimeter (ECL), which do not match any extrapolated charged track. To reduce the background from , we use a likelihood function that distinguishes an isolated photon from decays using the photon pair invariant mass, photon laboratory energy and polar angle kopenberg (). We reject both ’s in the pair if the likelihood probability is larger than 0.7. The reconstructed invariant mass of the () is required to satisfy 3.467 GeV 3.535 GeV (3.535 GeV 3.611 GeV). A mass-constrained fit is applied to the selected and candidates.
Charged kaons are identified by combining information from the central drift chamber, time-of-flight scintillation counters, and the aerogel Cherenkov counter systems. The kaon identification efficiency is while the probability of misidentifying a pion as a kaon is . mesons are reconstructed by combining two oppositely charged pions with the invariant mass lying between 482 MeV and 514 MeV. The selected candidates are required to satisfy the quality criteria described in Ref. goodks ().
To reconstruct candidates, each CX () is combined with a kaon candidate and a photon having 100 MeV (and not used in the reconstruction of ). If the invariant mass of any photon pair that includes this photon is found to be consistent with a (i.e., 117 MeV 153 MeV), this photon is rejected. Among the events containing at least one candidate, 9.0% have multiple candidates. In such cases, the forming the candidate with mass closest to the or masses pdg () is not used as the additional photon. This treatment suppresses reflections from the daughter photons.
The candidate is identified by two kinematic variables: the beam-constrained mass () and the energy difference (). Here, is the run-dependent beam energy, and and are the reconstructed energy and momentum, respectively, of the meson candidates in the center-of-mass (CM) frame. Candidates within a window of MeV and with 5.23 GeV are selected. Of these, 9.8% (6.4%) have multiple candidates in the () mode; we select the candidate with closest to zero. In order to improve the resolution in , we scale the energy of the so that is equal to zero. This corrects for incomplete energy measurement in the ECL. To suppress continuum background, events having a ratio of the second to zeroth Fox-Wolfram moments foxwolfram () above are rejected.
The and projections for the signal candidates are shown in Fig. 1, where a signal is evident. In addition, there is a significant narrow peak at 3823 MeV/, denoted hereinafter as . No signal of is seen. We extract the signal yield from a two-dimensional unbinned extended maximum likelihood (2D UML) fit to the variables and .
The resolution in () is parameterized by a sum of two Gaussians (Gaussian and logarithmic Gaussian lg ()). MC studies show that the resolutions in both and for a narrow resonance in the mass range 3.8 GeV 4.0 GeV are in good agreement with those for . The parameters of the resolution functions are determined from the MC simulation that is calibrated using the signal. We take into account the natural width pdg () by convolving the Breit-Wigner function and the resolution function; for the and , zero natural widths are assumed. The two-dimensional probability density function (PDF) is a product of the one-dimensional distributions.
For decays, the mean and width of the core Gaussian are floated and the remaining parameters are fixed according to MC simulations. To fit the signal, we float the mean of the core Gaussian but constrain the detector resolution by using the signal results after taking into account the difference estimated from the signal MC study. For , the parameters are fixed to those found for the , in accordance with expectations based on the MC simulation. For , we fix the mass difference and the mass resolution change with respect to using the information from PDG pdg () and MC studies. To fit , , , and , we fix all the parameters obtained from the signal MC study after correcting the PDF shapes by applying MC/data calibration factors.
To study background with a real , we use large MC simulated samples corresponding to 100 times the integrated luminosity of the data. The non- (non-) background is studied using () sidebands in data. In , the background with a broad peaking structure is mostly due to the , , and decay modes. produces peaks in both distributions ( and ), while the other backgrounds are flat in but peaked in . We determine the PDFs from the large MC sample. The fractions of the PDF components are floated in the fit, except for , whose fraction is controlled by fixing its ratio to the signal yield. For the combinatorial background, a threshold function, , where GeV (3.585 GeV) for (), is used for and an ARGUS function argus () is used for . The value of is estimated from a MC study; its variation, which affects the signal yield in the fits, is incorporated in the systematic errors. The data sidebands are used to verify the background PDFs. The fractions for the signal and the background components are floated in the fit.
The results of the fits are presented in Figs. 1-3 and in Table 1. The significance is estimated using the value of where () denotes the likelihood value when the yield is allowed to vary (is set to zero). In the likelihood calculation, the statistic uses the appropriate number of degrees of freedom (two in the case of and one for the other decay modes). The systematic uncertainty, which is described below, is included in the significance calculation cousinhighland (). We find a significant signal in all considered channels. We also obtain evidence for the in the channel with a statistical significance of 3.8 standard deviations (). The signals are insignificant. We estimate the branching fractions according to the formula ; here, is the yield, is the reconstruction efficiency, is the secondary branching fraction taken from Ref. pdg () and is the number of mesons in the data sample. Equal production of neutral and charged meson pairs in the decay is assumed. Measured branching fractions for the are in agreement with the world average values for all the channels pdg (). We set 90% confidence level (C.L.) upper limits (U.L.) on the insignificant channels using frequentist methods based on an ensemble of pseudo-experiments.
|Decay||Yield ()||(%)||Branching fraction|
A correction for small differences in the signal detection efficiency between MC simulation and data has been applied for the lepton and kaon identification requirements. Uncertainties in these corrections are included in the systematic error. The ( or ) and samples are used to estimate the lepton identification correction and the kaon (pion) identification correction, respectively. To estimate the correction and residual systematic uncertainty for reconstruction, samples are used. The errors on the PDF shapes are obtained by varying all fixed parameters by and taking the change in the yield as the systematic uncertainty. The uncertainties due to the secondary branching fractions are also taken into account. The uncertainties of the tracking efficiency and are estimated to be 0.35 per track and , respectively. The uncertainty on the photon identification is estimated to be 2.0%photon. The systematic uncertainty associated with the difference of the veto between data and MC is estimated to be 1.2% from a study of the sample.
To improve the mass determination of the , a simultaneous fit to and is performed, assuming that = . The peak position and resolution are common for both charged and neutral candidates. From this fit, we estimate the significance for to be 4.0 (including systematic uncertainties). We determine the mass of the signal peak relative to the well-measured mass :
Here, the first uncertainty is statistical and the second is systematic. Because of the mass-constrained fit to the candidate, the systematic uncertainty of is dominated by the additional photon’s energy scale. This photon energy scale uncertainty is estimated by the difference between the candidates’ mass without any constraint and the nominal mass pdg (), which results in 0.7 MeV as the systematic error. In order to estimate the width, we float this parameter and find no sensitivity with the available statistics: the width is MeV. Using pseudo-experiments generated with different width hypotheses for the , the U.L. at 90% C.L. on its width is estimated to be 24 MeV.
The mass of the is near potential model expectations for the centroid of the states: the Cornell cornell () and the Buchmüller-Tye buchmuller () potentials give 3810 MeV. Other models predict the mass of (the state, having ) to be 3815-3840 MeV Godfrey (); Ebert (); Eichten (); blank (). The mass agrees quite well with these models. In addition, since no peak has been seen around in the final state pakhlov (), one expects that does not decay to Eichten (). The ratio (at 90% C.L.) is consistent with the expectation () for pyungwon (); qiao (); Ebert (). The limited statistics preclude an angular analysis to determine the of the . The product of branching fractions for the is approximately two orders of magnitude lower than for the , as shown in Table 1; it is consistent with the interpretation of the as , whose production rate is suppressed by the factorization fact () in the two-body meson decays.
In summary, we obtain the first evidence of a narrow state, , that decays to with a mass of MeV and a significance of 3.8 , including systematic uncertainties. We measure the branching fraction product . No evidence is found for and we set an U.L. on its branching fraction product as well as the ratio 0.41 at 90% C.L. The properties of the are consistent with those expected for the state. We also determine an U.L. on the product of branching fractions, at 90% C.L.; this is less than one quarter of the corresponding value in pdg (). Our results show that the production of the ’s -odd partner in two-body decays and its decay to are considerably suppressed.
We thank the KEKB group for excellent operation of the accelerator; the KEK cryogenics group for efficient solenoid operations; and the KEK computer group, the NII, and PNNL/EMSL for valuable computing and SINET4 network support. We acknowledge support from MEXT, JSPS and Nagoya’s TLPRC (Japan); ARC and DIISR (Australia); FWF (Austria); NSFC (China); MSMT (Czechia); CZF, DFG, and VS (Germany); DST (India); INFN (Italy); MEST, NRF, GSDC of KISTI, and WCU (Korea); MNiSW and NCN (Poland); MES and RFAAE (Russia); ARRS (Slovenia); IKERBASQUE and UPV/EHU (Spain); SNSF (Switzerland); NSC and MOE (Taiwan); and DOE and NSF (USA). This work is partly supported by MEXT’s Grant-in-Aid for Scientific Research on Innovative Areas (“Elucidation of New hadrons with a Variety of Flavors”).
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