1. Recent BESII Results of Charmonium Decays Gang LI CCAST&IHEP, Beijing for Ψ(2S) Group Topical Seminar on Frontier of Particle Physics 2005: Heavy Flavor Physics August 13- 17, 2005

2. Outline  Introduction   cJ Study   ’ Decay to Multihadrons  Summary

3. Introduction  P-wave charmonium decays  c0,  c1,  c2 3M 14M 6.42 pb -1 data at Ecm=3.65 GeV for continuum study. 4M 2001.Nov.01to 2002.Mar.02

4.  cJ Study --- Motivation 1.Compared with J/ , relative little is known about P-wave triplet  cJ (J=0,1,2) decays, more data on exclusive decays of them are important for understanding of the nature of  cJ. 2. The decays of  cJ, in particular  c0 and  c2, provide a direct window on glueball dynamics in 0 ++ and 2 ++, as the  cJ hadronic decays may proceed via ccbar  gg  qqbar qqbar 3. PWA is an excellent tool to investigate the intermediate resonant decay account for the interferences when calculating Brs.

5. Partial Wave Analysis of  c0      K  K   cJ Study (I)

6. 1.  Q i = 0 ; 2. p(   )+p(   ) > 650 MeV [BG:  ’      J/  ]; 3. Prob(      K  K  )> Prob(          )& Prob(      K  K  )> Prob(  K  K  K  K  ); 4. M(     )  [497±50] MeV/c 2 & second vertex <5mm [BG: K S ]; Event level  c0      K  K  Avoid introducing a huge number of partial waves and also limited by statistics; our study is devoted to  c0      K  K  1371 events  c0  c1 (3511.3±1.3MeV)  c0 (3414.7±0.6MeV)  c2 (3556.4±0.9MeV) 5 C-fit dot with error bar :data

7. In our final fit, all these partial waves have been included, together with their interferences. For convenience of narration, we are to describe following decay modes one by one: 1.(     )( K  K  ) 2.(K    )(K    ) 3.(K   ) K

8. 1371 events (     )( K  K  ) f 0 (1710) f 0 (2200) f 0 (980) f 0 (1370)  (770)  S:change in log likelihood

9. S.Flatte, Phys. Lett. B 63(1976)224; B.S.Zou &D.V.Bugg, Phys. Rev. D48(1993)R3948 Flatte formula :  i (s)=sqrt(1-4m 2 i /s) : phase space factor for     &K  K  ; g i : squares of coupling constants to     &K  K  ; [ B.S.Zou &D.V.Bugg, Phys. Rev. D48(1993)R3948 ]: M=0.9535; g 1 =0.1108 GeV; g 2 =0.4229 GeV; For , formula once used by BES in analysis of J/        [ PLB598(2004)149-158] Other resonance s Breit-Wigner formula : (     )( K  K  )

10. Positive values indicate poorer fits Bad fit without scalar indicates that a scalar f 0 (2200) decays to K  K  is needed around 2.2 GeV. (     )( K  K  )

11. Results BES IIPDG2004 resonance Mass (M) and Width (  ) [unit:MeV] resonance Mass (M) and Width (  ) [unit:MeV] f 0 (1370)M:1265±30(+20–35)f 0 (1370)M:1200~1500  : 350±100(+105–60)  : 200 ~500 f 0 (1710)M:1760±15(+15–10)f 0 (1710)M:1714±5  : 125±25(+10–15)  : 140±10 f 0 (2200)M:2170±20(+15–10)  : 220±60(+10–15) Significance : 5. 3  Significance : 7. 1  Significance : 6. 5 

12. (K    )(K    ) 1371 events BW formula: with: m: mass of K  system; m 0 : mass of resonance;  0 resonance width; p: momentum of K in K  system; p 0 : p evaluated at resonance mass; r=3.4: Interaction radius[D.Aston et al., NPB296(1988)493] K* 0 (1430) K* 0 (1950) K*(892) 0

13. Results BES II PDG2004 resonance Mass (M) and Width (  ) [unit:MeV] resonance Mass (M) and Width (  ) [unit:MeV] K* 0 (1430)M:1455 ± 20 (+15 – 15)K* 0 (1430)M:1412 ± 6  : 270 ± 45 (+30 – 35)  : 294 ± 23 K* 0 (1950)M:1945 ± 30K* 0 (1950)M:1945 ± 10 ± 20  : ~500  : 201 ± 34 ± 79  #: 201 (fix to PDG in fit) Significance : 7. 1  Significance : 7. 2  Significance : 8. 7  (K    )(K    )

14. (K   )K 1371 events M(K  )  [896±60] M(   )  [700,800] K 1 (1270) K 1 (1400) K 1 (1279): S-wave BW K 1 (1400): S-wave BW 90% C.L. K 1 (1270)

15. Strange axial meson mixing (K   )K K 1 (1270) =K A sin  K + K B cos  K, K 1 (1400) = K A cos  K – K B sin  K, K A = K 1 (1270) sin  K + K 1 (1400) cos  K, K B = K 1 (1270) cos  K – K 1 (1400) sin  K, Here is an interesting problem involving K 1 (1270), K 1 (1400), that is the mixing of the two strange axial mesons In the quark model, there are two ground-state axial vector nonets, one is ( 3 P 1 ) state (K A ), the other is ( 1 P 1 ) state (K B ). For a strange quark mass is greater than those of up and down quarks, so SU(3) is broken which lead to mixing of K A and K B states to give a physical K 1 state: viz. or In SU(3) limit, only K A couples to the weak current, and the degenerated two octets before mixing lead to mixing angle (  K )equal to 45° which means that there should be equal amount of K 1 (1270) and K 1 (1400). Flavor-SU(3)-violating of K 1 (1270) -K 1 (1400) asymmetry is observed. However, our PWA yields : K 1 (1270)  K  [Br:(42±6)%] signal of 68.3±11.0 events; K 1 (1400)  K*  [Br:(94±6)%] signal of 19.7±6.9 events;

16. Strange axial meson mixing (K   )K Another interesting problem here is about the mixing angle  K. According to present BES results, the mixing angle  K >57º for  c0 More interesting fact is from  decay. By virtue of   K 1 measurement together with relativized quark model estimation, the mixing angle should be within a range: –35º<  K <45º at 68% C.L. [H.G.Blundell et al.,PRD53,3712(1996)] But according to previous BES results,  K <29º for  [PRL83,1918(1999)]  K >48º for J/  [PRL83,1918(1999)] All discrepancies displayed here indicate that more further theoretical and experimental works are needed.

17. Summary of PWA of  c0      K  K  Events: (1371-29) ; efficiency: (5.85 ± 0.01)% CLEO:PRD70, 112002(2004) B(K*(892)  K  )=100% = BES:PRD70, 09002(2004) B(  ’    c0   f 0 (980) f 0 (980)           ) =(6.5 ± 1.6 ± 1.3)  10 –5 B(  ’    c0 )=(9.22 ± 0.11 ± 0.46)  10 –3

18. Summary of PWA of  c0      K  K  (con’t) From these  c0      K  K  fit results, it is found that scalar resonances have larger decay fractions compared to those of tensors, and such decays provide a relatively clean laboratory to study the properties of scalars, i.e. f 0 (980),f 0 (1370),f 0 (1710), f 0 (2200), K* 0 (1430), and so forth. B(  ’    c0 )=(9.22 ± 0.11 ± 0.46)  10 –3 CLEO:PRD70,112002(2004)

19. First evidence of  c0, c2   cJ Study (II)

20. Kinematic fit  6-C fit is required, the additional 2-C is that two pair photons all satisfy M  =M  0, Furthermore,  2 (6C)<12 Prob(6C)> Prob(7C) is added if N  >5 so that the background from the potential  0,2   +    0  0 can be suppressed.  Removing the recoil J/  events by minimizing |M  +  - (recoil)-M J/  |, the recoiling mass of the candidate pion pair can’t fall into J/  peak region(3.08-3.12GeV). Event selection Some distributions in  0,2  from data Sideband region: 200 MeV wide around  peak Event level Signal region    c0  c2

21.  0  +    0  +    0  5  4  (  =1.66%) MC simulation    c0

22. Fit mass spectrum No obvious signal is found in sideband. M(  c0 )=3420.1±9.0MeV M(  c2 )=3553.3±11.9MeV (BW fit ;width fixed)  c0  c2 Background sideband N(  c0 )= 38.1  9.9 Sif. 4.4  N(  c2 )= 27.7  7.4 Sif. 4.7  (Mass & width fixed) dot with error bar :data The signal is described by BW convoluted with double-Gaussian obtained from MC simulations and background shape is determined by sideband shape.

23. Summary of  c0, c2  decay We first observed  0,2  decay and measure their branching ratios. We did not see obvious evidence below 3.2 GeV energy region.

24.  ’ decay to Multihadrons  ’  3(  +  - )  ’   +  -  0 K + K -

25.  Strong decay of  ’  3(  +  - ) suppressed due to G-parity violation.  e+e-  3(  +  - ) EM process (continuum contribution) will be estimated by off- resonance data @3.65 GeV.  X-sections @3.65 & 3.686 GeV give the EM form factor for 3(  +  - ) state.  BR of J/   2(  +  - ) determined via  ’   +  - J/ , J/   2(  +  - ).  ’  3(  +  - )

26. ψ’  π + π - J/ ψ, J/ψ  2(π + π - ) bkgd removed by requiring 3.06< <3.14 GeV M ππ 4C fit for ψ’  π + π - π + π - π + π - ψ’  KsKs π + π - bkgd removed by requiring 2 π + π - pairs satisfying 0.47<M ππ<0.53 GeV PRD71(2005)072006 Ks bkgd J/  bkgd

27.  ’  3(  +  - ) ψ’  3(π + π - ) @3.686 GeV Histogram = signal MC@3.686 GeV + continuum @3.65 GeV Hatched histogram = e + e -  3(π + π - ) DT@3.65 GeV 4C fit for π + π - π + π - π + π - final state e + e -  3(π + π - ) @3.65 GeV Histogram = MC simulation

28. BR of J/   2(  +  - ) Systematic error reduced by comparing 2 processes: Difference between MC & DT due to the simulation of error matrix in track fitting. Taken into account in systematic error. Confidence level distribution for kinematic fitting of    +  - J/ ,   2(  +  - )

29.  ’  3(  +  - ) RESULTS  ’  3(  +,  - ), J/   2(  +,  - ) BRs measured with improved accuracies. B[  ’  3 (  +,  - )]= (5.45  0.42  0.87) x 10 –4 greater than Mark I result (1.5  1.0) x 10 –4 {PRD17(1978)1731} B[J/   2(  +,  - )]= (3.53  0.12  0.29) x 10 –3 consistent with Mark I result (4.0  1.0) x 10 –3 {PRL 36(1976291} and BaBar result (3.61  0.26  0.26) x 10 –3 { hep-ex/0502025 } pQCD 12% rule tested. Q[3(  +,  - ) ]= (14  8)% Q[2(  +,  - ) ]= (13  3)% Form factors for e + e -  3(  +,  - ) at Ecm=3.65, 3.686 GeV determined F 3.65 [3(  +,  - ) ] = 0.19  0.02 F 3.686 [3(  +,  - ) ] = 0.24  0.02

30.  ’  +  -  0 K + K - PID for π and K 4C kinematic fit for  ’  +  - γγK + K - | -3.096 | >0.05 GeV/c to reject  ’  +  - J/  removed by identifying Ks  +  - Fit M(γγ) to obtain  ’  +  -  0 K + K - evts. Mγγ @ Ecm=3.686 GeV Mγγ @ Ecm=3.65 GeV  0 : 698  41 evts.  0 : 35  7 evts Preliminary

31.  ’  ωK + K - | Mγγ – 0.135 | <0.03 GeV/c 2 to select  ’  +  -  0 K + K - evts.  ’  ωK + K - evts are obtained by fitting M(  +  -  0 ). M(  +  -  0 ) @ Ecm=3.686 GeV M (  +  -  0 ) @ Ecm=3.65 GeV Preliminary ω: 78  11 evts. ω: evts.@68.3% C.L.evts.@68.3%

32.  ’  ωf 0 (1710) Dalitz plot for  ’  ωK + K - candidates M(K + K - ) for  ’  ωK + K - candidates Preliminary  ’  ωf 0 (1710) 18.9  6.2 evts.

33.  ’  +  -  0 K + K - Preliminary results ChannelB Ψ’  h (10 -4 )B J/Ψ  h (10 -4 ) Q h (%) K＋K－π＋π－π0K＋K－π＋π－π0 12.4  1.8 120  2810.3  2.9 ωK＋K－ωK＋K－ 2.38  0.47 16.8  2.114.2  3.4 ω f 0 (1710)  ωK ＋ K － 0.59  0.22 6.6  1.3 8.9  3.8

34. The PWA on  c0      K  K  in  ’    c0 decay is preformed. We fit the significant contributions from f 0 (980) f 0 (980), f 0 (980) f 0 (2200), f 0 (1370) f 0 (1710), K * (892) 0 K * (892) 0, K * 0 (1430) K * 0 (1430), K * 0 (1430) K * 2 (1430) +c.c. Flavor-SU(3)-violating of K 1 (1270)-K 1 (1400) asymmetry is observed and the mixing angle between two strange axial mesons is determined to be greater than 57 degree. First observed  c0, c2  decay and their branching ratios are measured. Summary

35. BRs of  ’  3(  +  – ), J/  2(  +  – ) with improved accuracy. F[3(  +  – )] determined at Ecm=3.65, 3.686 GeV. BRs of  ’   +  –  0 K + K – ;  ωK + K – ;  ωf 0 (1710)  ωK + K – with improved accuracy. Summary （ cont’d ）

36. Thanks a lot !