Charmonium[-like] states at Belle and BaBar\address
University of Maribor, Smetanova ulica 17, SI-2000 Maribor, Slovenia
Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana, Slovenia
Belle and BABAR experiments at the KEKB and PEP-II -factories provide also an excellent environment for spectroscopy studies. In this report we present recent results in the field of charmonium spectroscopy, focusing on new charmonium-like states observed in decays, and on resonances created in annihilation through the photon radiative return.
There has been a renewed interest in charmonium spectroscopy since 2002. The attention to this field was directed by the discovery of the two missing states below the open-charm threshold, and ,[1, 2] but even more by observations of a number of new particles  above the threshold for the open-charm production. Many of these exciting new states – although resembling charmonia – differ from regular states by some of their properties, or can simply not be identified as charmonia due to lack of available assignments. The naming convention, , , , already indicates lack of knowledge about the structure and properties of these new states at the time of their discovery.
The majority of these new states were observed by the
Belle  and BABAR  experiments,
operating their detectors at the two respective asymmetric-energy
colliders (so-called B-factories): KEKB in Japan and
PEP-II in the USA. Both experiments together have by now accumulated
huge data samples that in total correspond to nearly
and contain pairs.
2 Charmonium-like states observed in decays
The story about new charmonium-like states begins in 2003, when Belle
reported  on the analysis,
2.1 Charged charmonium-like states: ; &
Last year a surprising discovery of a new charmonium-like state was reported  by Belle in the analysis, performed on a data sample with pairs. After excluding the Dalitz regions that correspond to and mesons (i.e. veto), a strong enhancement is seen in the invariant mass distribution. A fit with a Breit-Wigner shape yields a peak mass and width of and , with a statistical significance. The observed resonance, called , is the first charged charmonium-like meson state – an obvious tetraquark candidate.
Using the same data sample as above, Belle also performed a full Dalitz plot analysis  with a fit model that takes into account all known resonances below . Dalitz plot is divided in five regions and the signal is clearly seen for the -veto-equivalent distribution, i.e. for the sum of the , and regions (see Fig. 2). The fit results with peak significance agree with previous Belle measurement, and provide the updated parameters: , and .
BABAR also searched for the signature in their data sample, analysing the ( = or ) decays. A substantial amount of work in this analysis is invested into a detailed study of the system, since its mass and angular-distribution structures strongly influence the Dalitz plots. As shown in Fig. 2 the invariant mass distributions are well described in terms of a superposition of , and wave amplitudes. The shapes and the composition of these components strongly affect the mass spectrum through the reflection background. However, it is found that these reflections alone can not explain a narrow peak in the or mass distributions. These distributions for all events, and separately for events inside and outside the and regions, are then fitted with the sum of the background function and a relativistic Breit-Wigner shape (see Fig. 2). No significant evidence for a signal peak is seen for any of the processes investigated, not even in the veto region for the distribution, where the was observed by Belle. The most prominent structure in the mass distribution for all events is an excess of with a mass and width of and . Using the Belle values  for the , the upper limit for the product of branching fractions is calculated as at a confidence level. This result gives no conclusive evidence for the existence of the , seen by Belle.
The observation of the state suggests that studies of decays could reveal other similar neutral and charged partners. Belle thus reports also on a Dalitz plot analysis of decays with pairs. The fit model for resonances is the same as in the Dalitz analysis, but here it includes also the meson. The fit results suggest that a broad doubly peaked structure in the invariant mass distribution should be interpreted by two new states, called and . The double- hypothesis is favoured when compared to the single- (no-) hypothesis by the statistical significance of (), and even with various systematic variations of the fit model, the significance is still at least (). The masses, widths and product branching fractions for the two states are: , , , ; and , .
2.2 Studies of states using ISR
The annihilation through initial-state radiation (ISR), , has proven to be a powerful tool to search for states at -factories: it enables a scan across a broad energy range below the initial centre-of-mass (CM) energy, while the high luminosity compensates for the suppression due to the hard-photon emission. The ISR processes are effectively identified by a small mass recoiling against the studied system . BABAR used this technique for a discovery of the state above threshold in the process. Using the same method Belle recently confirmed  the state, but also found another resonant structure, called . A similar analysis was performed by Belle to study the ISR annihilation process resulting in the final state. The obtained mass distribution reveals two resonant structures, called and . While still needs a confirmation, the former resonance, , has a mass similar to the wide structure , discovered previously by BABAR.
Results are summarised in Table 1. The states observed in and decay modes are distinctive, although a hint exists that the could also be seen in the decay mode. The nature of states and their strong couplings to are somewhat puzzling: such heavy charmonium(-like) states should decay mainly to , but it seems that observed states do not match the peaks in cross sections, measured by Belle. This conclusion is supported also by BABAR cross-section measurements.[27, 28]
|Y state||Decay mode||()||()||()||()|
3 Summary and Conclusions
The -factory experiments, Belle and BABAR, provide an excellent environment for charmonium spectroscopy. As a result, many new charmonium-like particles have been discovered during their operation, and some of them – like , , & and several states – are mentioned in this report.
- PEP-II was turned off in April 2008 and the final BABAR data sample corresponds to .
- In this review, the inclusion of charge-conjugated states is always implied.
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