aa r X i v : . [ h e p - e x ] N ov Proceedings of the CHARM 2007 Workshop, Ithaca, NY, August 5-8, 2007 Recent studies of Charmonium Decays at CLEO
H. Muramatsu
Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
Recent results on Charmonium decays are reviewed which includes two-, three- and four-body decays of χ cJ states, observations of Y(4260) through ππJ/ψ transitions, precise measurements of M ( D ), M ( η ) as well as B ( η → X ).
1. Introduction
Decays of a bound state of a quark and its anti-quark, quarkonium, provide an excellent laboratoryfor studying QCD. Particularly, heavy quarkonia suchas charmonium states are less relativistic, thus play aspecial role in probing strong interactions.CLEO recently has accumulated data taken at the ψ (2 S ) resonance, providing a total of 27M ψ (2 S ) de-cays. With the combination of this large statisticalsample and the excellent CLEO detector, we will ex-plore an unprecedented world of charmonia. Whilemany analyses are currently being carried out, in thisnote we present recent results on multi-body χ cJ de-cays which employed the pre-existing 3M ψ (2 S ) sam-ple.We also present recent studies on decays of one ofthe exotic states, Y(4260), as well as precision mea-surement on M ( D ) that has an implication on prop-erties of X(3872).Finally, based on the full sample of ψ (2 S ) data, wehave results on properties of one of the light mesons, η .
2. Factory of χ c (1 P J ) states χ c (1 P J ) states, which have one unit of orbital an-gular momentum and total spin of J=0, 1, or 2, can-not be produced directly from e + e − collisions. Theycan be reached from ψ (2 S ) through radiative (elec-tric dipole) transitions. Since B ( ψ (2 S ) → γχ cJ ) =(9 . ± . , . ± .
4, and 8 . ± . × − for J=0, 1,and 2 respectively [1], 27M ψ (2 S ) decays of the newdata provides ∼
2M decays of each spin state of χ cJ which should give us a greater understanding of thedecay mechanisms of the χ cJ mesons.In this section, we present recent results of studiesof χ cJ decays based on 3M ψ (2 S ) decays which shouldserve as the foundation for the future precision mea-surements by employing the full data sample of 27Mof ψ (2 S ) decays. We present results on χ cJ decay into combinationsof η and η ′ mesons. Figure 1 shows invariant masses of combinations of η and η ′ . No χ c is seen as expectedfrom conservation of spin-parity. Figure 1: Invariant masses of ηη (a), η ′ η (b), and η ′ η ′ (c) We measured B ( χ c → ηη ) to be (0 . ± . ± . ± . B ( ψ (2 S ) → γχ cJ ). This is slightly higher, but consistent with,the two previously published measurements. The BESCollaboration measured this branching ratio to be(0 . ± . ± . . ± . ± . B ( χ c → η ′ η ′ ) to be (0 . ± . ± . ± . B ( χ c → ηη ′ ) < .
05% , B ( χ c → ηη ) < . B ( χ c → ηη ′ ) < . B ( χ c → η ′ η ′ ) < . r , which is the ratioof doubly- to singly-OZI suppressed decay diagrams.In his model, our results indicate that the singly-OZIsuppressed diagram dominates in these decays. Proceedings of the CHARM 2007 Workshop, Ithaca, NY, August 5-8, 2007
We have also looked at three-body decays of χ cJ states (one neutral and 2 charged hadrons) [6]. Theyare π + π − η , K + K − η , p ¯ pη , π + π − η ′ , K + K − π , p ¯ pπ , π + K − K S , and K + ¯ p Λ. Measured branching fractionsare summarized in Table I. Again, our results are con-sistent with the results from BES Collaboration [7],with better precision.In three of the above modes we looked for, π + π − η , K + K − π , and π + K − K S , we observed significant sig-nals of χ c decays which are shown in Figure 2. Figure 2: Invariant masses of π + π − η (top-left), K + K − π (top-right), and K S K − π + (bottom) We performed Dalitz plot analyses based on these3 modes in which we neglected any possible interfer-ence effects between resonances and polarization of χ c . We estimated there could be ∼ ππη ( KKπ ) mode due tosuch a simplified model. Figure 3 shows the Dalitzplot for π + π − η and Table II shows its resultant fitfractions for each source. It is interesting to note thatour data demand a relatively large yield of a σ pole.As for the KKπ mode, we performed simultaneousfits between χ c → K + K − π and χ c → K S Kπ bytaking advantage of isospin symmetry. Dalitz plots forthese modes are shown in Figures 4 and 5. Table IIIshows their resultant fit fractions. We present a preliminary result on four-body decayof χ cJ states in which we reconstructed h + h − π π ,where h = π , K , p ; K + K − ηπ ; and K ± π ∓ K S π .Results of this kind of study, many-body decays of Figure 3: Dalitz plots for χ c → ηπ + π − .Figure 4: Dalitz plots for χ c → K + K − π . χ cJ states, should help to build a comprehensive un-derstanding about the P-wave dynamics.Clean signals were seen in all modes except χ c → p ¯ pπ π for the first time as can be seen in Figure 6.Many resonant substructures were also seen for whichwe only considered significant ones ( π + π − π π and K ± π ∓ K S π ). The results are summarized in Table V. roceedings of the CHARM 2007 Workshop, Ithaca, NY, August 5-8, 2007 Table I Branching fractions in units of 10 − . Uncertainties are statistical, systematic due to detector effects plusanalysis methods, and a separate systematic due to uncertainties in the ψ (2 S ) branching fractions. Limits are at the90% confidence level.Mode χ c χ c χ c π + π − η < .
21 5 . ± . ± . ± . . ± . ± . ± . K + K − η < .
24 0 . ± . ± . ± . < . p ¯ pη . ± . ± . ± . < .
16 0 . ± . ± . ± . π + π − η ′ < .
38 2 . ± . ± . ± . . ± . ± . ± . K + K − π < .
06 1 . ± . ± . ± .
14 0 . ± . ± . ± . p ¯ pπ . ± . ± . ± .
03 0 . ± . ± . ± .
01 0 . ± . ± . ± . π + K − K < .
10 8 . ± . ± . ± . . ± . ± . ± . K + ¯ p Λ 1 . ± . ± . ± .
06 0 . ± . ± . ± .
02 0 . ± . ± . ± . χ c → ηπ + π − Dalitz plot analysis.The uncertainties are statistical and systematic. Allowingfor interference among the resonances changes the fit frac-tions by as much as 20% in absolute terms as discussed inthe text. Mode Fit Fraction (%) a (980) ± π ∓ . ± . ± . f (1270) η . ± . ± . ση . ± . ± . χ c → πKK S . The measured branching fraction of χ cJ → ρ ± π ∓ π is consistent with that of χ cJ → ρ π + π − as ex-pected from isospin symmetry. Similar isospin sym-metry is also seen in Table IV where the partial width Table III Results of the combined fits to the χ c → K + K − π and χ c → πKK S Dalitz plots. Allowing for in-terference among the resonances changes the fit fractionsby as much as 15% in absolute terms as discussed in thetext. Mode Fit Fraction (%) K ∗ (892) K . ± . ± . K ∗ (1430) K . ± . ± . K ∗ (1430) K . ± . ± . a (980) π . ± . ± . of χ c → K ∗ K π and that of χ c → K ∗± K ∓ K are expected to be equal. Table IV also shows an-other good agreement with the isospin expectation of B ( χ c → K ∗ K π ) / B ( χ c → K ∗ K ± π ∓ ) = 0.5 and B ( χ c → K ∗ K π ) / B ( χ c → K ∗± π ∓ K ) = 0.5. Figure 6: Preliminary result on 4-body decays of χ cJ .Invariant masses of various combinations of hadrons areshown. Proceedings of the CHARM 2007 Workshop, Ithaca, NY, August 5-8, 2007
Table IV Branching fractions and combined error mea-surements for the isospin related K ∗ Kπ intermediatemodes are listed.Mode χ c χ c χ c B.F. (%) B.F. (%) B.F. (%) K ∗ K π ± ± ± K ∗ K ± π ∓ - - 0.90 ± K ∗± K ∓ π ± ± K ∗± π ∓ K ± ±
3. Charmonium-like states above D ¯ D3.1. Y(4260)
Y(4260) was first discovered by the BaBar Col-laboration via the reaction of e + e − → γY (4260) → γπ + π − J/ψ , J/ψ → ℓ + ℓ − [8]. Through the sameproduction mechanism of initial state radiation, wealso confirmed their observation based on data takenaround the Υ( nS ) resonances, where n is 1, 2, 3, and,4 [9]. The invariant mass of π + π − J/ψ based on suchISR production is shown in Figure 7.
Figure 7: Distribution of invariant mass of π + π − J/ψ pro-duced in ISR.
We further confirmed BaBar’s observation in datataken directly at √ s = 4260 MeV [10] at 11 σ sig-nificance. We also observed Y (4260) → π π J/ψ for the first time at significance of 5.1 σ and hadthe first evidence for Y (4260) → K + K − J/ψ (3 . σ ).We measured e + e − cross sections as σ ( π + π − J/ψ ) =(58 +12 − ±
4) pb, σ ( π π J/ψ ) = (23 +12 − ±
1) pb, and σ ( K + K − J/ψ ) = (9 +9 − ±
1) pb. Using scan data takenbetween √ s of 3970 MeV and 4260 MeV, we alsosearched in 12 additional modes (transitions down to ψ (2 S ), χ cJ , and J/ψ ). No evidence of strong signalswere seen for which we set upper limits at 90% confi-dence level. The results are summarized in Table VI. The observation of Y (4260) → π π J/ψ is inconsis-tent with the χ cJ ρ molecular model [11]. Our obser-vation of π π J/ψ rate being about half of π + π − J/ψ rate disagrees with the prediction of the baryoniummodel [12]. Evidence for the K + K − J/ψ signal is notcompatible with these two models either. Table VIalso shows that Y(4160) behaves very differently com-pared to other charmonium states above D ¯ D thresh-old such as ψ (4040) and ψ (4160) for which we set up-per limits in terms of cross section ( σ ( e + e − → X ))and branching fractions. Since X(3872) was discovered by Belle Collabora-tion [13] and subsequently confirmed by other exper-iments ([14],[15],[16]), many theoretical models havebeen proposed. Perhaps the most provocative theo-retical suggestion is that X(3872) is a loosely boundstate of D and ¯ D ∗ mesons [17]. This idea arisesmainly because M ( D ) + M ( D ∗ ) − M ( X (3872)) isvery small. Using the average value of M ( D ) of 2006Particle Data Group [1], 1864 . ± . − . ± . D and ¯ D ∗ mesons. The large uncertainty in the differ-ence is partially due to the rather large uncertainty inmass of D meson. This was the motivation to mea-sure M ( D ) more precisely using our 281 pb − of datataken at ψ (3770).We used a clean (charged particles only) mode ofD meson decay, D → K S φ where K S → π + π − and φ → K + K − . Invariant masses of π + π − and K + K − are shown in Figures 8 and 9 respectively. Fig-ure 10 shows the invariant mass of K S K + K − fromwhich we obtained M ( D ) = 1864 . ± . ± .
095 MeV [18]. We then have M ( D )+ M ( D ∗ )- M ( X (3872)) = +0 . ± . D and ¯ D ∗ mesons. The uncertainty in its binding en-ergy is now calling for more precise measurement onmass of X(3872) itself.
4. Properties of η It has been almost half a century since the η mesonwas discovered [19]. Since then, many measurementshave been made by many experiments. Still, almostall exclusive branching fractions are determined as rel-atives to other η decays.Based on the 27M ψ (2 S ) sample, we measured al-most all the major modes (99% of generic decays of η ) which allowed us to determine the major branch-ing fractions [20]. We obtained the η sample through roceedings of the CHARM 2007 Workshop, Ithaca, NY, August 5-8, 2007 Table V Branching fractions (B.F.) with statistical and systematic uncertainties are shown. The symbol “ × ” indicatesproduct of B.F.’s. The third error in each case is due to the ψ (2 S ) → γχ c branching fractions. Upper limits shownare at 90% C.L and include all the systematic errors. The measurements of the three-hadron final states are inclusivebranching fractions, and do not represent the amplitudes for the three-body non-resonant decays.Mode χ c χ c χ c B.F.(%) B.F.(%) B.F.(%) π + π − π π ± ± ± ± ± ± ± ± ± ρ + π − π ± ± ± ± ± ± ± ± ± ρ − π + π ± ± ± ± ± ± ± ± ± K + K − π π ± ± ± ± ± ± ± ± ± p ¯ pπ π ± ± ± < .
05 0.08 ± ± ± K + K − ηπ ± ± ± ± ± ± ± ± ± K ± π ∓ K π ± ± ± ± ± ± ± ± ± K ∗ K π × K ∗ → K ± π ∓ ± ± ± ± ± ± ± ± ± K ∗ K ± π ∓ × K ∗ → K π ± ± ± K ∗± K ∓ π × K ∗± → π ± K ± ± ± ± ± ± K ∗± π ∓ K × K ∗± → K ± π ± ± ± ± ± ± ρ ± K ∓ K ± ± ± ± ± ± ± ± ± e + e − → X , for three center-of-mass regions: the detection efficiency, ǫ ; the number of signal[background] events in data, N s [ N b ]; the cross-section σ ( e + e − → X ); and the branching fraction of ψ (4040) or ψ (4160)to X , B . Upper limits are at 90% CL. ’–’ indicates that the channel is kinematically or experimentally inaccessible. √ s = 3970 − √ s = 4120 − √ s = 4260 MeVChannel ǫ N s N b σ B ǫ N s N b σ B ǫ N s N b σ (%) (pb) (10 − ) (%) (pb) (10 − ) (%) (pb) π + π − J/ψ
37 12 3.7 9 +5 − ± < +4 − ± < +12 − ± π π J/ψ
20 1 1.9 < < +5 − ± < +12 − ± K + K − J/ψ – 7 1 0.07 < < +9 − ± ηJ/ψ
19 12 9.5 < < < < < π J/ψ
23 2 < < < < < η ′ J/ψ – 11 4 2.5 < < < π + π − π J/ψ
21 1 < < < < < ηηJ/ψ – – 6 1 < π + π − ψ (2 S ) – 12 0 < < < ηψ (2 S ) – – 15 0 < ωχ c – – 9 11 11.5 < γχ c
26 9 8.1 < <
11 26 11 8.7 < <
10 26 1 3.3 < γχ c
25 6 8.0 < <
17 26 10 8.6 < <
18 27 4 3.3 < π + π − π χ c < <
11 8 0 < < < π + π − π χ c < <
32 8 0 < <
13 9 0 < π + π − φ
17 26 3.0 < < < < < a two-body decay of ψ (2 S ), ψ (2 S ) → ηJ/ψ where J/ψ subsequently decays to two leptons ( e + e − or µ + µ − ).That is, we have sample of about 0.1M η decays witha di-lepton tag on J/ψ .We first constrained the invariant mass of di-leptonsto be the known mass of
J/ψ . We then combinedthe fitted
J/ψ with η decay products and constrained further to be the mass of ψ (2 S ). In this analysis,the η decay modes we considered were η → γγ , 3 π , π + π − π , π + π − γ and e + e − γ . According to Ref. [1],the sum of these 5 rates amounts to 99 .
88% of thetotal η decays. We then took ratios between efficiency-corrected yields separately for each of J/ψ → e + e − and µ + µ − cases in which all lepton related systematic Proceedings of the CHARM 2007 Workshop, Ithaca, NY, August 5-8, 2007
Figure 8: Invariant mass of π + π − .Figure 9: Invariant mass of K + K − . uncertainties were canceled. The resulting ratios of η branching fractions are summarized in Table VII.Figure 11 shows a graphical version of comparisonin terms of ratios of branching fractions to the singlemost precise other measurements (top of Figure 11).By assuming that the 5 exclusive channels we con-sidered in this analysis cover the all η decay modes, wewere also able to extract absolute branching fractionsof these 5 modes. Other possible η decay modes areeither now allowed and/or found to be less than 0 . η [1]. We included 0 .
3% as a possi-ble systematic uncertainty in the absolute branchingfraction measurements. The results are summarizedin Table VIII and also shown graphically in Figure 11in terms of ratio of our branching fractions to the PDG2006 global fit (bottom of Figure 11). Several of therelative and absolute branching fractions obtained inthis analysis are either the most precise to date or firstmeasurements.Further more, we also measured the mass of η me- Figure 10: Invariant mass of K S K + K − .Table VII Ratios of η branching fractions. For each com-bination, the efficiency ratio, separately for J/ψ → e + e − and J/ψ → µ + µ − , the level of consistency between the J/ψ → e + e − and µ + µ − result, expressed in units of Gaus-sian standard deviations, σ µµ/ee , and the combined resultfor the branching ratio. The dagger symbol indicates thatthis result is most precise measurement to date.Channel eff. ratio σ µµ/ee branching fraction ratio µµ ee π /γγ .
15 0 .
15 1 . ± ± pi + π − π /γγ .
50 0 . − . ± ± † π + π − γ/γγ .
63 0 .
60 0 . ± ± † e + e − γ/γγ .
53 0 .
52 0 . ± ± † π /π + π − π .
30 0 .
32 2 . ± ± † π + π − γ/π + π − π .
27 1 .
24 1 . ± ± e + e − γ/π + π − π .
07 1 .
06 0 . ± ± † e + e − γ/π + π − γ .
84 0 .
86 0 . ± ± son [22]. This was motivated by two recent preci-sion measurements that were inconsistent with eachother. In 2002, the NA48 Collaboration reported M η = 547 . ± . ± .
041 MeV [23], while in 2005,GEM Collaboration reported M η = 547 . ± . ± .
032 MeV [24] which was 8 standard deviations belowNA48’s result.We used the same η sample described previously inthis Section but used only 4 decay modes, η → γγ ,3 π , π + π − π , and π + π − γ while, again, constrain-ing masses of J/ψ and ψ (2 S ). Our result, the av-erage of the 4 η decay modes, is M η = 547 . ± . ± .
057 MeV which has comparable precisionto both NA48 and GEM results, but is consistentwith the former and 6.5 standard deviations largerthan the later. We note that the KLOE Collabora-tion also recently measured mass of the η meson to be547 . ± . ± .
031 MeV which was presented atthe 2007 Lepton-Photon conference [25]. roceedings of the CHARM 2007 Workshop, Ithaca, NY, August 5-8, 2007 Table VIII For each η decay channel, absolute branchingfraction measurements for J/ψ → e + e − and J/ψ → µ + µ − combined, with statistical and systematic uncertainties(middle column), as determined in this work. The lastcolumn shows the PDG fit result [1]. All but γγ are firstmeasurements.Channel this work (%) PDG [1] (%) γγ . ± . ± .
36 39.38 ± π . ± . ± .
49 32.51 ± π + π − π . ± . ± .
29 22.7 ± π + π − γ . ± . ± .
14 4.69 ± e + e − γ . ± . ± .
05 0.60 ±
5. Summary
I have presented confirmation of BaBar’s observa-tion of Y(4260) in di-pion transition to
J/ψ alongwith a new observation through neutral di-pion tran-sition. Our precision measurement on M ( D ) calls formore precise measurement on M ( X (3872)). With 3M ψ (2 S ) sample, we have results on two-, three-, andfour-body decays of χ cJ states in which many sub-structures were seen in three- and four-body modes.Dalitz plot analyses were done for the case of 3-bodydecays. More detailed analyses can be done with thefull 27M ψ (2 S ) sample. Using the 27M sample, weperformed precision measurements on B ( η → X ) and M ( η ). References [1] W. M. Yao et al. [Particle Data Group], J. Phys.G , 1 (2006).[2] G. S. Adams et al. (CLEO Collaboration), Phys.Rev. D , 071101(R) (2007).[3] J. Bai et al. (BES Collaboration), Phys. Rev. D , 032004 (2003).[4] M. Andreotti et al. (E-835 Collaboration), Phys.Rev. D , 112002 (2005).[5] Q. Zhao, Phys. Rev. D , 074001 (2005).[6] S. Athar et al. (CLEO Collaboration), Phys. Rev.D , 032002 (2007). [7] M. Ablikim et al. (BES Collaboration), Phys.Rev. D , 072001 (2006).[8] B. Aubert et al. ( BaBar
Collaboration), Phys.Rev. Lett. , 142001 (2005).[9] Q. He et al. (CLEO Collaboration), Phys. Rev.D , 091104 (2006).[10] T. E. Coan et al. (CLEO Collaboration), Phys.Rev. Lett. , 162003 (2006).[11] X. Liu, X.-Q. Zeng, and X.-Q. Li, Phys. Rev. D , 054023 (2005).[12] C.-F. Qiao, he-ph/0510228 (2005).[13] S. K. Choi et al. (Belle Collaboration), Phys. Rev.Lett. , 262001 (2003).[14] D. Acosta et al. (CDF II Collaboration), Phys.Rev. Lett. , 072001 (2004).[15] V. M. Abazov et al. (D ∅ Collaboration), Phys.Rev. Lett. , 162002 (2004).[16] B. Aubert et al. ( BaBar
Collaboration), Phys.Rev. D , 071103 (2005).[17] E. S. Sanson, Phys. Lett. B588 , 189 (2004); N.A. T¨ornqvist, Phys. Lett.
B599 , 209 (2004); M.B. Voloshin, Phys. Lett.
B579 , 316 (2004).[18] C. Cawlfield et al. (CLEO Collaboration), Phys.Rev. Lett. , 092002 (2007).[19] A. Pevsner et al. , Phys. Rev. Lett. , 421 (1961).[20] A. Lopez et al. (CLEO Collaboration), Phys.Rev. Lett. , 122001 (2007).[21] M. Ablikim et al. (BES Collaboration), Phys.Rev. D , 052008 (2006); D. Alde et al. , Z. Phys. C25 , 225 (1984); Yad. Fiz. , 1447 (1984); R. R.Akhmetshin et al. (CMD-2 Collaboration), Phys.Lett. B509 , 217 (2001); J. J. Thaler et al. , Phys.Rev. D , 2569 (1973).[22] D. H. Miller et al. (CLEO Collaboration), Phys.Rev. Lett. , 122002 (2007).[23] A. Lai et al. (NA48 Collaboration), Phys. Lett. B533 , 196 (2002).[24] M. Abdel-Bary et al. (GEM Collaboration),Phys. Lett.
B619 , 281 (2005).[25] F. Ambrosino et al. (KLOE Collaboration),arXiv:0707.4616 (contributed paper to LeptonPhoton 2007).