Properties of non- mesons and results of a search for the -dibaryon
A number of charmonium- and bottomonium-like meson states have been observed that have properties that do not match well to expectations for the simple quark-antiquark substructure suggested by the constituent quark model. Some of them are electrically charged and decay to final states containing hidden charmonum or bottomonium mesons and, thus, must contain at least four quarks. Common properties of these so-called mesons are partial widths for decays to hidden quarkonium states plus light hadrons that are much larger than corresponding partial widths for established quarkonium mesons. I review some recent results from the Belle experiment, including the recent discovery of two charged bottomium-like states, the and , that decay to () and () final states. In addition, I present recent Belle results from a search for -dibaryon production in inclusive and decays.
Properties of non- mesons and results of a search for the -dibaryon
Stephen Lars Olsen††thanks: Speaker.
Department of Physics & Astronomy, Seoul National University
Gwanak-gu, Seoul, 151-747, KOREA
According to the prescriptions of the original quark model proposed by Gell-Mann  and Zweig  in 1964, mesons are comprised of quark-antiquark pairs and baryons are three-quark triplets. In the 1970’s, this simple model was superseded by Quantum Chromodynamics (QCD), which identified the reason for these rules was that pairs and combinations can be color singlet representations of the color group that is fundamental to the theory. Somewhat suprisingly, the mesons are and baryons are prescription still adequately describes the hadronic particle spectrum despite the existence of a number of other color-singlet quark and gluon combinations that are possible in QCD . Considerable experimental efforts at searching for the predicted color-singlet “pentaquark” baryons  and the doubly strange -dibaryon  have failed to come up with any unambiguous candidates for either state . Although a few candidates for non- light hadron resonances have been reported  none have been generally accepted as established by the hadron physics community .
In recent years, however, the situation changed, beginning with the observation of the meson by Belle , the discovery of the meson by BaBar , and the subsequent observation of a number of other candidate charmonium-like meson states, the so-called mesons, that are not well matched to expectations for the quark-antiquark meson picture . Here I give a brief report on why we think the observed states may be exotic and describe some recent observations of charged quarkonium-like meson states that necessarily must have a minimal four-quark structure by Belle [12, 13, 14] and BESIII .
In 1977, Jaffe predicted the existence of The -dibaryon, a doubly strange, six-quark structure () with quantum numbers and and a mass that is MeV below the . An , baryon-number particle with mass below would decay via weak interactions and, thus, be long-lived with a lifetime comparable to that of the and negligible natural width.
Jaffe’s specific prediction was ruled out by the observation of double- hypernuclei events [18, 19, 20], especially the famous “Nagara” event that has a relatively unambiguous signature as a He hypernucleus produced via capture in emulsion . The measured binding energy, MeV, establishes, with a 90% confidence level (CL), a lower limit of MeV, severely narrowing the window for a stable to the binding energy range MeV111In this report I have taken the liberty of averaging asymmetric errors and combining statistical and systematic errors in quadrature. For actual measured values, please refer to the original papers.
Although Jaffe’s original prediction for a binding energy of MeV has been ruled out, the theoretical case for an -dibaryon with a mass near continues to be strong and has been recently strengthened by lattice QCD calculations (LQCD) by the NPLQCD [21, 22] and HALQCD  collaborations that both find a bound -dibaryon, albeit for non-physical values for the pion mass. NPLQCD’s linear (quadratic) extrapolation to the physical pion mass gives MeV ( MeV) . Carames and Valcarce  recently studied the with a chiral constituent model constrained by , , and cross section data and find values that are similar to the NPLQCD extrapolated values.
2 The Quarkonium Spectra
Quarkonium mesons, i.e., mesons that contain a and quark pair, where is used to denote either the - or -quark, have proven to be useful probes for multiquark meson systems. That is because these mesons are well understood; their constituent quarks are non-relativistic and potential models can be applied. Most of the low-lying meson states have been discovered and found to have properties that agree reasonably well with potential model predictions. More complex states would likely have properties that deviate from model predictions and, thus, be identifiable as such.
Figure 2 shows a level diagram for the (“charmonium”) system, where established states are indicated by solid lines, and the masses predicted by the Godfrey-Isgur (GI) relativized potential model in 1985  are shown as dash-dot lines. All of the states below the open-charmed-meson threshold have been identified and have masses that agree reasonably well with GI predictions. Moreover, all of the above-threshold states below GeV have been assigned and, here too, there is reasonable agreement with predicted masses. In addition to the states, the , the radially excited state, has been assigned  and Belle recently reported strong evidence for the , the state . Any meson state with prominent decays to final states containg a - and a -quark, that does not fit into one of the remaining unassigned states has to be considered exotic.222 The large value of the -quark mass precludes any substantial production of pairs via fragmentation processes.
Figure 2 shows a level diagram for the (“bottomonium”) system. Here all the levels indicated by solid bars are well established. In addition, the have been recently reported of the , and [31, 32], as well as evidence for some of the (unshown) -wave and states . Three states above the open-bottom threshold have been tentatively identified as the , and , and these are their commonly used names. The arrows in Fig. 2 indicate transitions between the sates accompanied by either light-hadron emission (vertical arrows) and electromagnetic transitions (diagonal arrows). Not shown are the -transition that was used by BaBar to discover the , the and transitions used by Belle to discover the states , or the transition that led to the discovery of the . With the notable exception of the and transitions, which are anomalously strong and discussed below, all of the other transitions have measured strengths that are consistent with theoretical expectations.
The first meson that was observed is the , which was seen as a pronounced peak in the invariant mass spectrum in exclusive decays [9, 35]. Decays to [36, 37, 38], [36, 39], and  have also been seen. The invariant mass distribution in decays is well described by the hypothesis that the pions originate from decays [41, 42]. A CDF analysis of angular correlations among final state particles in ruled out all possible assignments (for ) other than and . A Belle analysis of angular correlations in ; decays found good agreement with the hypotheses with no free parameters; for there is one free complex parameter and a value for this was found that produces acceptable agreement with the measured data . Recently, an comprehensive analysis of the five-dimensional angular correlations in the , , decay chain conclusively ruled out the assignment and established, once and for all, that the of the is .
The only unassigned charmonium level with a predicted mass near 3872 MeV is the , the first radial excitation of the . The assignment of the to this level has some problems. First, the mass is too low. Potential models predict the mass of the to be around 3905 MeV, where this is pegged to the measured mass of the multiplet-partner state MeV . If the mass is 3872 MeV, the - mass splitting would be MeV, and higher than the - mass splitting of MeV. In potential models this splitting decreases with increasing radial quantum numbers . Second, the decay is a favored transition and expected to be more than an order-of-magnitude stronger than “hindered” transition . The Belle experiment recently reported a 90% CL limit on that is less than  and in contradiction with potential model expectations for the assignment. Third, the transition , the discovery mode, violates isospin and is expected to be strongly suppressed.
Two features of the that have attracted considerable attention are its narrow natural width, MeV at the 90% CL , and its mass, for which (my) world average value is MeV, which is equal, to about a part in , to the mass threshold: MeV. The close proximity of the to the threshold has led to speculation that the is a molecule-like - bound state held together by nuclear-like - and -meson exchange forces .
The was seen by BaBar as a peak in the distribution in the initial-state-radiation (ISR) process , an observation that was confirmed by CLEO and Belle . Since it is produced via the ISR process, its must be . In contrast to the , the peak is relatively wide; the weighted average of the BaBar and Belle peak width measurements is MeV.
A striking feature of the is that its peak mass is not near that of any of the established charmonium states. Moreover, since all charmonium states with mass below MeV have been identified, the cannot be a standard meson. Moreover, it does not seem to have a strong coupling to open-charm mesons; measurements of annihilation into charmed mesons in the vicinity of MeV show indications of a dip in the total cross section at the location of the peak . This motivated a detailed analysis  that established a lower limit on the partial width that is greater than 1 MeV, which is huge for charmonium. The Belle group did a comprehensive search for decays to all possible final states containing open charmed meson pairs and found no sign of a signal in any of them . Thus, it seems likely that the is substantially greater than 1 MeV. If this is the case, it would be a strong indication that some new, previously unanticipated, mechanism is involved.
Subsequent studies of the ISR process led to discoveries of states with similar characteristics decaying to the final state: the by BaBar , and the by Belle . There is no evidence for open-charmed meson decays for either of these states. Moreover, there is no sign of them in the spectrum and is there no evidence for .
4 Searches in the -quark sector
The existence of the and other hidden charm states with large partial widths to and led to speculation that there may be counterparts in the -quark sector . This prompted a Belle measurement of the partial widths for (). The expected branching fraction for these decays  is and, with the data sample that was available at the time, the expectation was that no signal would be seen. (The measured branching fractions for the nearby to are less than .) Rather remarkably, very strong signals were observed for all three decays modes, with branching fractions of nearly one percent — more than two-orders-of-magnitude times expectations . In an attempt to determine whether or not the anomalous events were coming from decays of or from some other, -quark sector equivalent of the lurking nearby, Belle did a cross section scan of hadrons and  . This scan showed some indication that the yield peaks at a mass distinct from that for hadrons but with limited statistical significance ( MeV for the three channels vs. MeV for inclusive hadrons).
4.1 Study of inclusive plus anything
Motivated by the curious phenomena described in the preceding section, Belle made a study of the inclusive process plus anything . Figure 3 shows the missing mass recoiling against every pair in events in a 121 fb data sample collected at an c.m. energy in the vicinity of the resonance. In this plot there are a huge number of entries, on the order of a million in each of the 1 MeV bins; the relative statistical error on each point is of order . The distribution is fitted piecewise to a polynomial background shape plus signal peaks for all of the bottomonim states (and reflections) that are expected to be produced via this process.
Figure 4 shows the results of the fit with the background component subtracted. There, in addition to peaks corresponding to () and reflections from the ISR processes , (), are distinct signals for and with and significance, respectively, and a hint of . This is the first observation of the and bottomonium states. The prominent signals – similar in strength to the signals – are somewhat surprising because the process requires a -quark spin-flip and is expected to be supressed.
The huge number of events in the and signal peaks in Fig. 4 ( K and K events, respectively) permitted an investigation of the resonant substructure in decays. Figure 5(a) shows the yield determined from fits to the recoil mass spectrum for different values of mass, determined from missing mass measurements of the signals in bins of the mass recoiling against one of the pions. Figure 5(b) shows the corresponding mass distribution.
As is evident from the figures, the and signals are entirely due to two structures in , one with peak mass near MeV and the other with peak mass near MeV. In the following, these structures are referred to as the and , respectively. The histograms in each figure show the results of fits to the mass spectra using two Breit Wigner (BW) amplitudes to represent the peaks plus a phase-space component. The fitted results for the BW parameters for the two peaks, which are consistent with being the same for both decay channels, are listed below in Table 1. For both spectra, the fitted strengths of the phase space term are consistent with being zero.
4.3 distributions in decays
Belle also made an investigation of possible resonant substructure in fully reconstructed decays () . Figure 6 shows the (vertical) vs. (horizontal) Dalitz plot for decays. Here, to avoid double counting, only the highest mass combination is plotted. In the figure there is a sharp vertical band at small masses caused by background from converted photons, and two distinct horizontal clusters near GeV and GeV, near the locations expected for the and . The and Dalitz plots show similar structures.
The Dalitz plots are fitted with a model that includes BW amplitudes to represent the two states, terms that account for possible contributions in the system from the and resonances, and a non-resonant amplitude using a form suggested by Voloshin . The regions of the Dalitz plots contaminated by photon conversion backgound (i.e. to the left of the vertical line in Fig. 6) are excluded from the fits. and projections with the results of the fits superimposed are shown in Fig. 7 and included in Table 1. The and mass and width measurements from the five different channels agree within their errors. The averages of the five mass and width measurements for the are MeV and MeV; for the , the averages are MeV and MeV. These are very near the MeV and MeV mass thresholds, respectively, which is suggestive of virtual molecule-like structures , although other interpretations have been proposed .
4.4 The transitions and the discovery of the
In studies of bottomonium physics, the - mass difference has special importance since this determines the scale of the spin-spin hyperfine interaction term in the potential. This is accessible to Lattice QCD calculations, which give values that from MeV to MeV . The was discovered by the BaBar collaboration in the radiative process . BaBar produced the first measurement of the splitting to be MeV, which is outside the theoretical range. This measurement was an experimental tour-de-force because the environment is very difficult, with a weak signal and substantial backgrounds that make the extraction of a precise mass value difficult.
The Belle observation of strong signals for and in inclusive decays, provides another way to access the , and that is via the transitions, . Figures 8(a) and (b) show the and signal yields determined from fitting the -recoil mass spectra, but this time in bins of missing mass. In this measurement, s that are not associated with a decay are combined with the pairs to determine , which is plotted on the horizontal axis . Distinct peaks near GeV corresponding to the are evident in both distributions. These data are used to determine the hyperfine splitting MeV and total width MeV. This measurement of has improved precision and has a central value that is about higher than the BaBar measurement and within the range of theoretical expectations.
Figures 8(c) shows the signal yields determined from fitting the recoil spectrum in bins in the mass range expected for the , where a prominent peak can be seen near GeV. Belle identifies this as the first observation of the and measures MeV.
As mentioned above, the LQCD calculations of produce a range of values that reflect the different approximations that are necessary for managable lattice calculations. On the other hand, in ratios of the splittings between different radial states, many of these uncertainties cancel. Thus, at least for the time being, measurements of these ratios present the strongest challenges for theory. The Belle measurement of the ratio is in agreement with a LQCD prediction of .
5 Search for the -dibaryon in and decays.
As mentioned in the intoduction above, recent theoretical results motivate searches for the with mass near the threshold. This mass region is especially interesting, because very general theoretical arguements ensure that for masses approaching the threshold from below, the would behave more and more like a analog of the deuteron, and for masses approaching from above, the would look more and more like a virtual dineutron resonance, independently of its dynamical origin . If its mass is below , the would predominantly decay via weak transitions to , , or final states. If its mass is above , but below MeV), the would decay via strong interactions to 100% of the time.
Decays of narrow () bottomonium () resonances are particularly well suited for searches for deuteron-like multiquark states with non-zero strangeness. The states are flavor- singlets and primarily decay via the three-gluon annihilation process (e.g., (% ). The gluons materialize into , and pairs in roughly equal numbers. The high density of quarks and antiquarks in the limited final-state phase space is conducive to the production of multi-quark systems, as demonstrated by large branching fractions for inclusive antideuteron () production: and . An upper limit for the production of a six-quark state in decays that is substantially below that for the six-quark antideuteron would be strong evidence against its existence.
Belle recently completed a search for -dibaryon production in the inclusive decay chains ; and , using data samples containing 102 million and 158 million decays. The search strategy assumed equal and branching fractions: i.e., .
The resulting continuum-subtracted () distribution for the combined and samples, shown in the top (bottom) left-hand panels of Fig. 9, has no evident () signal. The curve in the figure is the result of a fit using a threshold function to model the background; fit residuals are also shown. The dashed curves in the figures show the expected signal for a branching fraction that is that for antideuterons.
The panels on the right of Fig. 9 show the (above) and (below) distributions for events that satisfy the selection requirements. Here there is no sign of a near-threshold enhancement similar to that reported by the E522 collaboration  nor any other evident signal for (). The curve is the result of a background-only fit using the functional form described above; fit residuals are also shown. Expectations for a signal branching fraction that is that for the antideuterons is indicated with a dashed curve.
In the absence of any sign of an -dibaryon in either the or the mode, we set the 90% CL ()-dependent branching fraction upper limits for the and (for ) mode shown in Figure 10. These limits are all more than an order of magnitude lower than the average of measured values of , shown in Fig. 10 as a horizontal dotted line.
These new Belle results are some of the most stringent constraints to date on the existence of an -dibaryon with mass near the threshold . Since hadrons decays produce final states that are flavor- symmetric, this suggests that if an -dibaryon exists in this mass range, it must have very different dynamical properties than the deuteron, or, in the case of , a strongly suppressed decay mode.
After years of theoretical and experimental work, a large assortment of particles, the mesons, have been found that can not be accounted for by the standard mesons are quark-antiquark pairs rule that has been in common practice. There are now almost twenty candidates, a number that continues to grow rapidly. Many of these new mesons are close to particle-antiparticle thresholds and look very much like molecular structures of color-singlet mesons, however others are far from thresholds, which make molecular assignments less compelling. One feature of these states are their strong decays to hidden quarkonium states. In cases where partial width measurements have been possible, the results are usually much larger than those measured for conventional quarkonium states. Likewise, decays to open-flavor states seem to be suppressed compared to those for quarkonium mesons.
Few of the observed states were predicted in advance by theorists, while some predicted states, such as charged partners of the have been searched for but not been seen . Moreover, none of the new particles make compelling matches to any of the states that are predicted by the QCD-motivated models that theorists seem to really like. The experimental limits on pentaquarks and the -dibaryon keep getting more stringent with no compelling signs for either of them. Attempts have been made to attribute some of the states to diquark-diantiquark color bound states , however, these models predict that these structures should form flavor- multiplets and, so far at least, no multiplet partners of the observed states have been found.
This remains very much an experiment-dominated field of research. Hopefully as the list of states expands and the properties of the established states are better know, some pattern will emerge that will allow someone to make sense of it all.
I thank the organizers of this meeting for inviting me to present these results. In addition I compliment them on their well organized and interesting meeting. This work is supported by the Korean national Research Foundation via Grant No. 2011-0029457 and WCU Grant No. R32-10155.
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