Bled Workshops in Physics Vol. 9, No. 1
Proceedings of the Mini-Workshop Few-Quark States and the Continuum Bled, Slovenia, September 15-22, 2008

p. 78
Charm and Charmonium Spectroscopy at Belle
M. Bracko, representing the Belle Collaboration
University of Maribor, Smetanova ulica 17, SI-2000 Maribor, Slovenia Jozef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana, Slovenia
Abstract. The Belle experiment at the KEKB asymmetric-energy e+ e- collider provides an excellent environment not only for B physics, but also for studies in charm and charmonium spectroscopy. Most important Belle achievements in this field include observations of several yet undiscovered particles and measurements of their properties. In this paper we report and briefly discuss most recent of these experimental results.
1	Introduction
The Belle detector [1] at the asymmetric-energy e+ e- collider KEKB [2] has accumulated about 850 fb-1 of data by July 2008. The KEKB collider is called a B-factory; it operates with a peak luminosity that exceeds 1.7 x 1034 cm_2s_1 at the T(4S) resonance, slightly above the BB-production threshold, and the accumulated data set contains a large number of BB pairs. Although both B-factories—a similar collider called PEP-II delivers data to the BABAR detector—were initially designed for measurements of CP violation in the B-meson system, it was soon clear that excellent detector performance and large amount of experimental data also enable searches for new charm and charmonium states as well as studies of their properties.
2	Excited charmed strange mesons (Dsj)
The interest in Dsj mesons received a boost after recent discoveries of two states: D*0(2317) + in D+n0 decay mode1 and Ds1 (2460)+ in D*+n0 mode, both observed with continuum e+e~ —> cc events by the BABAR [3] and CLEO [4] collaborations, respectively. Belle confirmed the existence of the two states in continuum events [5], but also in B —> DDsj decays [6]. An angular analysis performed in the latter case, favours the JP = 0+ and 1+ values for D*0 (2317)+ and Ds1 (2460) +, respectively.
Due to the Ds meson in their final state, the states D*0 (2317)+ and Ds1 (2460) + are most naturally interpreted as P-wave excited cs states with j = |L + S-| = 1 /2, where |L| = 1 is the orbital angular momentum and Sj- is the spin of the
1 Charge-conjugated modes are implied, unless explicitly stated otherwise.
light s-antiquark. Nonetheless, while the masses and widths of previously observed Ds1 (2536)+ and Ds2 (2573)+ are in relatively good agreement with potential model predictions, both the masses and widths of D*0 (2317)+ and Dsi (2460)+ states are smaller than expected (see Ref. [7] for a discussion of cs models). Additionally, the mass difference between the two newly observed states is much larger that the difference between the masses of Ds1 (2536)+ and Ds2 (2573) +. All these properties have led to interpretations of the Ds0(2317)+ and Ds1 (2460) + as four-quark states or at least as states with significant four-quark content. Experimentally, these interpretations could be tested in decays B° —» D+jK~, where the initial B°-meson quark content (bd) is completely different from the one in the D+jK~ final state (cssu). However, Belle results [8] were not conclusive about the four-quark content of D*0 (2317)+ and Dsi (2460)+, but at least supported the claim that these two states do not belong to the same spin-doublet.
2.1 Observation of a new state Dsj (2700) +
Fig.l. Left: Dalitz plot for B+ —» D°D°K+ decays. Centre: B meson signal yield versus M(D°K+) for M(D°D°) > 3.85 GeV/c2. The solid curve denotes the total fit result, while the dotted curve shows the sum of non-Dsj (2700)+ components—including the ^ (4160) reflection on the right. Right: Efficiency corrected Dsj (2700)+ helicity-angle distribution together with predictions for various spin hypotheses: J = 0 (dotted line), 1 (solid line) and 2 (dashed line).
In order to obtain further experimental data and help resolve the issues for Dsj states, Belle recently performed an analysis of the B+ —» D°D°K+ decays using a data sample containing about 449 • 106 BB pairs [9]. A study of the Dalitz plot for the AE-Mbc signal region2 (see the left-most plot in Fig. 1) revealed that the decay B+ —» D°D°K+ proceeds dominantly via quasi-two-body channels: B+ ->i|>(3770)K+ and B+ -> D°DsJ (2700) + . While the observed rate for i|>(3770) production in B meson decays is consistent with our previous observation [10],
2 The two kinematic variables identify B-meson candidates: AE = Eb — Ebeam and Mbc = 1 /c2 y^-beam ~~ (Pbc)2, where Eb and pb are the energy and momentum of the B candidate, and Ebeam is the beam energy, all expressed in the centre-of-mass (CM) frame.
the Dsj(2700)+ is a previously unobserved resonance in the D0K+ system (see the central plot in Fig. 1) with a mass of M = (2708 ± 9—0) MeV/c2 and a width of r = (108 ± 23—If) MeV/c2. The observed decay mode and angular analysis (see the right-most plot in Fig. 1) clearly favour the interpretation of Dsj(2700) + as a cs meson with Ip = I-. The new meson could be a cs radially excited 23Si state [11] with a mass of (2710 - 2720) MeV/c2 or the 1— chiral partner [12] of the Ds i (2536)+ meson with a mass of (2721 ± 10) MeV/c2. Additional measurements are needed for the new meson to distinguish between the two existing interpretations.
2.2 Dsi (2460)+ - Dsi (2536)+ Mixing
Another interesting result on Dsj mesons comes from the recent study [13] of Ds i (2536)+ mesons, produced inclusively in e+ e— —> Ds i (2536) + Xanything reactions. The analysis is based on the e+e— continuum data set corresponding to 462 fb—1 and uses two decay modes for a Ds 1 (2536)+ reconstruction, namely Ds 1 (2536)+ —> D+n—K+ and Ds 1 (2536)+ D*+K°. The observed invariant mass MD + n-K+ and the invariant mass difference MDon+Ko — MDon+ for all selected D+n—K+ and D0n+KS combinations are shown in Fig. 2. The ratio of branching fractions of the two studied decay modes is found to be: B(Ds1 (2536) + D+n—K+)/B( D0n+K0) = (3.27±0.18±0.37)%. The decay channel Ds1 (2536) + —> D+n—K+ is only the second observed three-body decay mode of the Ds1 (2536) + meson (after Ds1 (2536)+ D+n+n—) [14].
The large and clean Ds1 (2536)+ —> D*+K^ sample enables a partial-wave analysis for this decay mode. Heavy Quark Effective Theory (HQET) predicts that for an infinitely heavy c-quark the D*+K^ decay of the |JP = 1+; j = 3/2} state, Ds1 (2536)+, should proceed via a pure D-wave [15]. The same decay of its partner Ds1 (2460)+, the |1 +; 1 /2} state, would proceed via a pure S-wave—if this was energetically allowed. Since the heavy quark symmetry is not exact, the two states can mix, and an S-wave component can appear in the decay Ds1 (2536)+ —> D*K. Even if mixing is small, the S-wave contribution to the total width can be sizeable, since the D-wave contribution is strongly suppressed by the small energy release in this decay. Using a small polarization of Ds1 (2536)+ mesons produced in e+e— annihilations and performing a simultaneous fit to the three angles in the decay Ds1 (2536)+ —» D*+K^; D*+ —» D0n+, the measurement shows that the S-wave actually dominates. Its contribution to the total width in the decay Ds1 (2536)+ —> D*+ K° is rS/rtotal = 0.72 ± 0.05 ± 0.01. This result indicates there is a mixing between the two states: Ds1 (2536)+ and Ds1 (2460) +.
3 Charmonium and Charmonium-like States
There are several possible mechanisms of the charmonium(-like) particle production at B-factories: production in the B-meson decays, formation of C-even states in yy processes and in e+e~ annihilation into J/i[>(cc), and creation of Jpc = 1 ~~ resonances in e+ e- annihilation after the photon radiative return. Several of these
Fig.2. Invariant mass spectra of selected D + n-K+ (Top) and Dp+ KS (Bottom) combinations. The hatched histogram in the top plot shows the spectrum of wrong sign D + n+ K- combinations. The M(Dp+G) in the bottom denotes the Dp+ nominal mass from Ref. [14].
m(ja|j 11) [gev/c2)
Fig.3. Invariant mass distributions of J/^n+ n- combinations for B+ —> K+ X(3872) (Top) and B0 -> KSX(3872) (Bottom) decay candidates. The fit results are shown with solid curves.
charmonium(-like) particles have been recently discovered. The naming convention for these new X, Y, Z states indicates the lack of knowledge about their structure and properties at the time of discovery.
3.1 The X(3872) news
In 2003 Belle reported on the B+ —> K+J/^n+n- analysis [16], where a narrow charmonium-like state X(3872) decaying to J/^n+n- was discovered, and soon confirmed by CDF, D0 and BAB4R [17]. In PDG2006 [14], the world average of the mass is (3871.2 ± 0.5) MeV/c2 and the upper limit on its width, as measured by Belle, is 2.3 MeV. X(3872) does not appear to be a simple charmonium state and its quantum numbers are not yet determined. The observed X(3872) —> yJ/^ decay [18] (implying C = +1) as well as results of angular analyses [19,20] and studies of J/^n+n- kinematical properties favour JPC = 1++ and 2 + assignments. The latter possibility could have been ruled out by the study of B —> KD°D°7t° decays, where a near-threshold enhancement for the D°D°7t° invariant mass was observed at (3875.4 ± 0.7 ± 1.1) MeV/c2 [21]. However, since the invariant mass of the DD7T peak was about 2a higher than the world average value for X(3872), this result encouraged speculations about the two similar states, as predicted by a four-quark model of X(3872)[22]. Another interpretation of X(3872), a D°D*°
Fig.4. The n+ ^(2S) invariant mass distribution for events in the AE-Mbc signal region. The shaded histogram shows the scaled contribution from the AE sideband, while the solid curves correspond to the fit result.
Fig.5. The mass distributions for n- J/^ (Top) and n+ n-^(2S) (Bottom) combinations from e+ e- annihilation with the ISR photon. The curves show the fit and contributions of individual resonances for constructive (Solution I) and destructive (Solution II) interference.
molecule, is strongly motivated by the fact that the X(3872) mass is very close to the D°D*° threshold [23].
Belle recently reported on the updated X(3872) analysis, using the data sample of 657-106 BB pairs [24].X(3872] —> J/i[>7T+7T~ decays are reconstructed in both charged and neutral B decays (see Fig. 3), and the observed ratio of the branching fractions, B(B0 —> KgX(3872))/B(B+ K+X(3872)) = 0.82 ± 0.22 ± 0.05, isofthe order of unity. Comparison of the neutral and charged B-meson signal can serve as a test for the four-quark hypothesis of X(3872), which predicts the existence of two four-quark states—ccuu should be produced mainly in charged and ccdd in neutral B-meson decays—with a mass difference of AM = (8 ± 3) MeV/c2 [22]. In contrast to this expectation, no mass difference between the X(3872) candidates in charged and neutral B-meson decay is observed: AM = (0.18 ± 0.89 ± 0.26) MeV/c2. The measurements therefore favour the charm-meson molecular interpretation of X(3872), although the virtual state of two charm mesons is also not excluded [25].
3.2 Charged charmonium-like state: Z+ (4430),...
Recently a new charged state was observed by the B —> Kn±^(2S) Dalitz analysis, performed on a data sample with 657 • 106 BB pairs [26]. Both charged and neutral B decays are used, and the ^(2S) candidates are reconstructed in four decay modes: e+e-, |j.+ |j.-, and J/^n+n- with J/^ —> e+e-, |j.+ |j.-. After excluding the Kn Dalitz regions that correspond to K*(890) and K2(1430)
Table 1. Properties of JPC = 1 states (Y resonances) observed by Belle using the ISR technique.
Tstate Decay mode M (MeV/c2) F (MeV) Y(4008) J/ipTt+Tt" 4008 ± 40—¡4 226 ±44 ±87 Y(4260) J/^n+ 4247 ± 12+17 108 ± 19 ± 10 Y(4360) ^(2S)n+ 4361 ± 9 ± 9 74 ± 15 ± 10 Y(4660) ^(2S)n+ 4664 ± 11 ± 5 48 ± 15 ± 3
mesons, a strong enhancement is seen in the n+^(2S) invariant mass distribution (Fig. 4). A fit with a Breit-Wigner shape yields a peak mass and width of (4433 ± 4 ± 2) MeV/c2 and (45— if—f°) MeV, with a 6.5ct statistical significance. The observed resonance called Z+ (4430)—if confirmed by other experiments— would be the first charmonium-like meson candidate with non-zero charge, and could be interpreted as a charged molecular or a four-quark state. Systematic studies of B —> K7t(cc) decays could reveal other similar neutral and charged partners [22]. During the preparation of this paper, a study was already reported, indicating the existence of a broad doubly peaked structure in the 7t+xci mass for exclusive B° —> K~7t+xci decays [27],
3.3 Study of JPC = 1 — states using ISR
Initial-state radiation (ISR) has proven to be a powerful tool to search for 1 —— states at B-factories, since it allows to scan a broad energy range of a/s below the initial e+ e— CM energy, while the high luminosity compensates for the suppression due to the hard-photon emission. With the ISR technique, BABAR discovered Y(4260) state above D,*)D,*> threshold in the e+e~ -}> yiSRY(4260) -}> YISRJ/^n+n— process [28].
Using the same method as BABAR on a data sample of 548 fb—1, Belle recently confirmed the Y(4260) state, but also found another resonant structure, called Y(4008) (see the top plot of Fig. 5)[29]. A similar analysis was performed on a 673 fb—1 data sample to study the ISR e+ e— annihilation process resulting in the ^(2S)n+n— final state [30]. The obtained ^(2S)n+n— mass distribution, shown in the bottom plot of Fig. 5, reveals two resonant structures, called Y(4360) and Y(4660). While Y(4660) still needs a confirmation, the former resonance, Y(4360), has a mass similar to the wide structure at (4324 ± 24) MeV/c2, observed previously by BABAR[31]. Fit results for Belle measurements are summarized in Table 1. The four Y states observed in J/^n+n— and ^(2S)n+n— decay modes are distinctive, although there is a hint that Y(4260) could also be seen in the ^(2S)n+n— decay mode [32]. The nature of Y states and their strong couplings to J/^n+n— and ^(2S)n+ n— are somewhat puzzling: such heavy charmonium(-like) states should decay mainly to D' *1D' *1, but it seems that observed Y states do not match the peaks in e+ e— —> d(*)±d(*)t cross sections, measured by Belle with ISR at V^<5GeV[33].
Fig.6. Left: J/^DW recoil mass distribution, showing peaks at D, D* and D*n mass. Histograms show the scaled D '*' sidebands; curves indicate the total fit result (solid) and the background component (dashed). Right: The D(*1D(*1 mass distributions for e+ —> J/t|)D(*1"D(*1 events.
3.4 Double cc production in e+e annihilation
Belle observed a surprisingly large double charmonium production in a study of the J/^ and ^(2S)(—> J/^n+ n-) recoil mass3 spectrum for inclusive e+ e- —> T/tJjX processes [34], The extracted e+e~ —> J/i[)(cc) cross-section was more than five times larger than values from the tree-level QCD calculation and still represents a challenge for theorists. The J/^ recoil method was further improved
Table 2. Properties of two states observed in double cc production. Significance includes systematic uncertainties.
X state Decay mode M (MeV/c2) F (MeV) Significance (a) X(3940) DD1*1 3942+g ± 6 37+^f±8	57
X(4160) D^'D1*1 4156+^ ± 15 139+^ ±21 5.1
and used for studies of C = +1 charmonium states above DD threshold. A D(+) meson besides the J/^ is reconstructed, and a constraint Mrecoii(J/^D(*)) ~ M(DppG) is then applied to select e+e~ —> T/tJjD(*)D'*' events (see the recoil mass distributions in Fig. 6). As a result of this method, two states, X(3940) and X(4160), were identified in the DD* and D*D* distributions, respectively [35,36]. The fit results for the two peaks, shown in Fig. 6, are summarized in Table 2. Possible interpretation for these states include conventional nc(3S) and Xco(3P) charmonia.
3 E.g. the J/tJj recoil mass, Mrecoii( J/tJj) = 1 /c2^/(ECm — E*)2 — (cp*)2, is calculated in the CM frame with the total event energy (Ecm) and J/^ energy and momentum (E* and p*).
4 Summary and Conclusions
The Belle experiment at the KEKB collider provides an excellent environment for charm and charmonium spectroscopy. As a result, many new particles have already been discovered during the Belle operation, and some of them — like DsJ(2700)+, X(3872), X(3940), X(4160) and Z+ (4430)— are mentioned in this report. As new experimental data are still accumulated and many studies are ongoing, more interesting results on charm and charmonium spectroscopy are to be expected from Belle in the near future.
The Belle experimental results have already raised a lot of interest among theoretical physicists. Various interpretations for the nature and properties of newly observed states have been proposed. Some of the answers might be found in the near future, perhaps following also the ideas presented at this workshop.
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