Charmonium spectroscopy and decays
In this talk, I review the recent experimental developments on charmonium. These mainly include the precision measurements of spin-singlet states , , , studies of the charmonium-like states and the states. Charmonium transitions and decays are also discussed.
Charmonia are charmed-quark and anticharmed-quark states () bound by the strong interaction. Charmed quarks are heavy, so the motion of the charm quark inside the bound state is slow, , where is relative velocity between the and . The charmonium system can be approximately considered as a non-relativistic bound state. The energy levels can be found by solving a non-relativistic Schrodinger equation, with sophisticated corrections (e.g. relativistic correction) and other effects. Figure 1 shows the charmonium levels from this approach Godfrey:1985xj (). Although all charmonium states below the mass threshold have been observed, knowledge is sparse on spin-singlet -wave (), the (), and the -wave (). Above the threshold, the spin-triplet -wave states , and , and the -wave , and have been found. The , , , are commonly assigned as (), (), () and (), respectively. The observed by Belle Uehara:2005qd () in the mass distribution from events, is identified with ().
Information about the spin-dependent interaction of heavy quarks can be obtained from precise measurement of the hyperfine mass splitting , where MeV/ PDG () is the spin-weighted centroid of the mass and is the mass of the singlet state . A non-zero hyperfine splitting may give an indication of non-vanishing spin-spin interactions in charmonium potential models swanson ().
With 106M events, BESIII observed clear signals in the recoil mass distribution for with and without the subsequent radiative decay Ablikim:2010rc (), as shown in Fig. 2. They reported first measurements of the absolute branching ratios and , along with improved measurements of the mass . They found the hyperfine mass splitting to be , which is consistent with no strong spin-spin interaction. The results are in agreement with CLEO-c’s earlier results Dobbs:2008ec ().
In addition, BESIII used 16 exclusive hadronic decay modes to reconstruct . By doing so, the ratio of signal to background can be improved significantly. A simultaneous fit to the recoil mass distributions of the 16 decay modes was performed. From 106M events, signal events are found. The measured mass and width are , and , which are consistent with the inclusive analysis results, and also consistent with CLEO-c’s results Dobbs:2008ec ().
The radially excited spin-singlet -wave state, the meson, was not well established until the Belle collaboration found the signal at in the invariant mass distribution in a sample of exclusive decays Choi:2002na (). Since then measurements of in photon-photon fusion to final state have been reported Aubert:2003pt (); Asner:2003wv (); Nakazawa:2008zz (), as well as in double charmonium production Aubert:2005tj (); Abe:2007jn (). CLEO-c searched for in the radiative decay , found no clear signals in its sample of 25M :2009vg (). The challenge of this measurement is the detection of 50 photons.
With 519 fb, BaBar observed and produced in photon-photon fusion for the first time delAmoSanchez:2011bt (). They measured the mass and width of and in decays, , , , . These results are so far the most precise measurements.
Belle updated the analysis of and followed by and decay to with 535 million -meson pairs :2011dy (). Both decay channels contain the backgrounds from decays without intermediate charmonia, which could interfere with the signal. Belle’s analysis took interference into account with no assumptions on the phase or absolute value of the interference. A two dimensional – fit was performed to extract signal, where is the angle between (from directly) with respect to in the rest frame of the . They obtained the masses and widths of and . For the meson parameters the model error is negligibly small: MeV/, MeV/. For the meson the model and statistical uncertainties cannot be separated: MeV/, MeV/.
Using 106 million events, BESIII searched for in the decay , with . Figure 3 shows the invariant mass distribution of , where a three-constraints kinematic fit has been applied (in which the energy of the photon is allowed to float). The solid curve in Fig. 3 shows preliminary results of an unbinned maximum likelihood fit with four components: signal, , and other background (coming from decays to , and ISR/FSR production of ). The fit, in which the width of the is fixed at 12 MeV, yields signal events, and gives the mass . The statistical significance of the signal is more than 6. Using the detection efficiency determined from MC simulation, the product branching fraction is obtained . Using the result from BaBar Aubert:2008kp () gives the branching fraction . This result is consistent with CLEO-c’s upper limit :2009vg () and predictions of potential models Eichten:2002qv ().
The mass and width of the lowest lying charmonium state, the (), continue to have large uncertainties when compared to those of other charmonium states PDG (). Early measurements of the properties of the using radiative transitions Baltrusaitis:1985mr (); Bai:2003et () found a mass and width of and , respectively. However, recent experiments, including photon-photon fusion and decays, have reported a significantly higher mass and a much wider width Aubert:2003pt (); Asner:2003wv (); Uehara:2007vb (); belle2011 (). The most recent study by the CLEO-c experiment, using both and , pointed out a distortion of the line shape in decays recent:2008fb (). CLEO-c attributed the line-shape distortion to the energy dependence of the “hindered” transition matrix element.
At BESIII, the can be produced through , and the mass and width are determined by fits to the invariant mass spectra of exclusive decay modes. Six modes are used to reconstruct the : , , , , , and , where the is reconstructed in , and the and in decays. Figure 4 shows the invariant mass distributions for selected candidates, together with the estimated backgrounds ( represents the final states under study), the continuum backgrounds normalized by luminosity, and other decay backgrounds estimated from the inclusive MC sample. A clear signal is evident in every decay mode. The signal has an obviously asymmetric shape that suggests possible interference with a non-resonant amplitude. The fitted relative phases between the signal and the non-resonant component from each mode are consistent within , which may suggest a common phase in all the modes under study. A fit with a common phase (i.e. the phases are constrained to be the same) describes the data well. The preliminary results on the mass and width are , .
Figure 5 compares the recent measurements of the and mass and width from two photon-photon fusion, transition, and decays. These results are in good agreement. Hyperfine splittings are , and . which agree well with recent lattice computations Burch:2009az ().
The was first observed as a narrow peak in the invariant mass spectrum near threshold from decays by Belle Choi:2003ue () in 2003, and later confirmed by BaBar Aubert:2008gu (). The decay was also observed inclusively in prompt production from collisions at the Tevatron by both CDF Acosta:2003zx () and D0 Abazov:2004kp (). CDF studied the angular distributions and correlations of the final state, found that the dipion was favored to originate from , and thus only assignments of and explained their measurements Abulencia:2006ma ().
A number of theoretical models have been proposed for the states, such as conventional charmonium state, molecules, diquark-diantiquarks, -gluon hybrids etc., but none can comfortably account for all experimental results. Charmonium states and are possible candidate states for the . For a state, a large branching fraction is expected; experimental results do not agree. For a state, a large width is expected; but the observed is narrow. In the molecule model it is hard to explain the large radiative decay rate, the rate and the production in . The diquark-diantiquarks model predicts partners for the , but no partner has been found yet. For -gluon hybrids, the mass is too low.
The mass of
With 2.4 fbdata, CDF presented an analysis of the mass of the reconstructed via its decay to Aaltonen:2009vj (). They found 6K candidates, shown in Fig. 6. They measured the mass , which is the most precise determination to date. In EPS2011, LHCb presented measurements of the mass of with 35 pb data. Belle also updated the mass and width measurements with 711 fb data Choi:2011fc (). A new world average that includes these new measurements and other results that use the decay mode is .
An important feature of the is its mass is close to the threshold. A possible interpretation is that the is a molecule-like arrangement comprised of a and a Voloshin:2003nt (); Tornqvist:2004qy (). Crucial to these models is whether the mass is above or below . Taking the and mass from PDG 2010, . The new world average is lower than , as shown in Fig. 7.
Search for partners
Models of tightly bound diquark-antidiquark system feature two neutral and one charged partner states Maiani:2004vq (). The , observed in decays, is interpreted as a combination. In , one should see a partner state, the combination. The two states differ in mass by a few . In addition, a neutral partner and a charged () partner are also expected by isospin and flavor-SU(3).
BaBar Aubert:2008gu () and Belle Choi:2011fc () measured the mass for and decays, separately. They found mass differences that are consistent with zero, for Belle, and for BaBar. The possibility that the enhancement in is composed of two different narrow states, and , was addressed by CDF Aaltonen:2009vj (). By fitting their 6000 event peak with two different Gaussian functions, they found and have masses closer than 3.6 MeV for equal and production.
BaBar searched for a charged partner of the in the mass distribution from decays, and found no evidence for a signal in either or decays Aubert:2004zr (). They determined the upper limits , at 90% CL. The Belle limits for the same quantities at 90% CL are , Choi:2011fc (). The results rule out the isospin triplet model for the .
Using a data sample of 465 million pairs, BaBar searched for decays, found evidence for and X(3872) with 3.6 and 3.5 , respectively :2008rn (). They measured the product of branching fractions and , and obtained the ratio . The relatively large branching fraction of is generally inconsistent with a purely molecular interpretation of the , and possibly indicates mixing with a significant component.
With 772 million events, Belle observed in the charged decay with a significance of , while in a search for no significant signal was found Bhardwaj:2011dj (). They measured the branching fractions , and provided upper limit on the branching fraction . The upper limit on the ratio was (at 90% CL).
This results of from Belle and BaBar are consistent, while the results are in disagreement. More data is need to confirm these results.
The production characteristic of the in collisions, such as the and rapidity distributions and the ratio of prompt production versus production via -meson decays, are very similar to those of the well established charmonium state Abazov:2004kp (). Thus it is of interest to compare production characteristics of the to those of other charmonium states in meson decays. One common characteristic of all of the known charmonium states that are produced in meson decays is that when they are produced in association with a pair, the system is always dominated by a strong signal.
Belle studied the production in association with a in decays Istomin:2008tj (). In a sample of 657M pairs, about 90 signal events are seen. Figure 8 shows the invariant mass distribution for these events, where it is evident that most of the pairs have a phase space like distribution, with little or no signal for . All of the events in the peak seem to be due to the side-band determined background. This is contrasted to the events (with ) in the data sample, where the invariant mass distribution, shown in Fig. 9, is dominated by the .
The state remains a mystery. Better understanding demands more experimental constraints and theoretical insight.
, the first unexpected vector charmonium-like state, was observed by BaBar Aubert:2005rm () in ISR production of . CLEO He:2006kg () and Belle :2007sj () confirmed the BaBar result, but Belle also found an additional broader structure at 4008 . BaBar found Aubert:2006ge () another enhancement, in , which Belle measured with larger mass and smaller width, Belle also found :2007ea () a second structure near 4660 .
There is only one unassigned charmonium state in this mass region, the , and no room to accommodate all of the four observed peaks. Figure 10 shows the cross sections. No enhancement is seen for any . The absence of any evidence for () decays to open charm implies that the () partial width is large. Ref. Mo:2006ss () gives keV at 90% CL, an order of magnitude higher than expected for conventional vector charmonium. Charmonium would also feature dominant open charm decays, exceeding those of dipion transitions by a factor expected to be , as is the case for the and .
At the EPS2011 conference, Belle presented an analysis of . They measured ev, which is about half of the ev PDG (). This is consistent with the CLEO’s study Coan:2006rv () on direct production of in collisions. It implies that the has , as expected for a state.
The decay ,
The study of vector charmonium decay to a photon and neutral pseudoscalar meson provides experimental constraints on the relevant QCD predictions, such as the vector meson dominance mode(VDM), two-gluon couplings to states, mixing of . The ratio is predicted by first order perturbation theory, and is also expected Chernyak:1983ej (). However, CLEO-c reported measurements for the decays of , and to , and no evidence for or was found :2009tia (). Therefore, they obtained with at 90% CL. Such a small is unanticipated, and it poses a significant challenge to our understanding of the bound states. Do other processes contribute? Is this related to the puzzle Appelquist:1974zd ()?
With 106M events, BESIII observed and and , where is reconstructed from and , and is reconstructed from and Ablikim:2010dx (), as shown in Fig. 11. The measured branching fractions are summarize in Table. 1. The is about 20 times smaller than . for each decay mode is also shown in the table, which is much smaller than 12%.
(a) Mass (GeV/)
The decay ,
events make significant contributions to the radiative decays of . The decay of the P wave to provides a good chance to validate theoretical predictions and search for glueballs Amsler:1995td (). CLEO-c found Bennett:2008aj () a surprisingly large branching fraction, an order of magnitude higher than the pQCD prediction Gao:2006bc (). With 106M events, BESIII studied the decays , with representing , and Ablikim:2011kv (). The results are listed in Table 2, where the decay is the first observation. The results provide tight constraints on QCD.
Vector pair decay modes are measured at BESIII :2011ih (). In the analysis, candidates are reconstructed with , and , respectively. The helicity selection rule suppressed decays are observed for the first time and there is an evidence of the doubly OZI suppressed decay with a significance of 4.1.
Charmonium is the best understood hadronic system. All the lowest-lying charmonium states have been found; the long-anticipated states have been measured with high precision, good agreement between their measured properties and theory. Higher-mass charmonium meson searches have produced surprises; unanticipated states showed up.
Enormous progress has been achieved on charmonium decays. Many expected decays and transitions have either been measured with high precision or for the first time.
Belle, BaBar, CLEO, CDF and D0 have produced fruitful results in the past. LHC is starting to produce physics results. Large data samples from LHC will allow identification of the X, Y, Z states, and measurements of production, and polarization. BESIII will continue to study charmonium physics. Future experiments, such as PANDA, will complement the activities at other labs.
Acknowledgements.This work is supported in part by the Ministry of Science and Technology of China under Contract No. 2009CB825200;
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