1. Zijin Guo University of Hawaii (Representing BES Collaboration) Quarkonium Working Group ’04, IHEP Beijing October 13, 2004 Study of  c Decays at BES

2. OUTLINE Introduction  cJ  pp,   cJ  h + h - KsKs  cJ  K * (892) 0 K * (892) 0  c0  f 0 (980)f 0 (980)  c2 polarization Summary  

3. INTRODUCTION Charmonium System

4. Exclusive quarkonium decays contribute an important laboratory for investigating QCD. Compared to J/  decays, relatively little is known concerning PC = ++  cJ decays. Color octet mechanism (COM) important for P-wave quarkonium decays. A consistent set of theoretical predictions for the branching fractions, as well as more precise experimental measurements will lead to a better understanding of the COM and the nature of  cJ states. Furthermore, the decays of  cJ, in particular  c0 and  c2, provide a direct window on glueball dynamics in the 0 ++ and 2 ++ channels. C. Amsler and F. Close, PRD53 (1996) 295

5. World  (2S) Samples (×10 6 )  (2S) BESII Detector

6. Color octet mechanism (COM) important for P-wave quarkonium decays. G. T. Bodwin et al., Phys Rev. Lett. D51, 1125 (1995). H.-W. Huang and K.-T. Chao, Phys. Rev. D54, 6850 (1996). J. Bolz et al., Phys. Lett. B392, 198 (1997). Color octet graphs (qqg) Color singlet graphs (qq) for  CJ → .  cJ  pp,  

7.  (2S)   cJ   ΛΛ   p  - p  +  Clear Λ Λ-bar signal Monte Carlo Data  cJ   

8.  c0  c1  c2 B  cJ   (10 –4 )4.7 ± 1.02.6 ± 0.63.3 ± 0.7 +1.3 -1.2 +1.0 -0.9 +1.5 -1.3 PRD67, 112001 (2003) Sideband background Data/Monte Carlo  cJ signal  c0  c1 c2c2 

9.  c0  c2  c1 Final states:  pp  cJ  pp 

10. COM for  cJ  B B Discussion Many systematic errors cancel! Calculate The results on  c1 and  c2 decays only agree marginally with model predictions. No prediction for  c0. Phys.Rev.D69:092001,2004

11.  cJ → K S K S  cJ →  +  - K S K S BESII Preliminary  cJ  h + h - KsKs  (2S)   cJ  cJ → K + K - K S K S

12. BESII Preliminary  The branching fractions of  cJ decays to  +  - K S K S and K + K - K S K S are observed for the first time.  The branching fractions of  c0 and  c2 decays to K S K S are measured with improved precision.

13. Measure more decays to better understand P-wave decays. Study χ cJ → K * (892) K * (892) → K + K -  +  - Require Prob(  2 4C ) > 1% and higher than  +  -  +  - and K + K - K + K - cases, and PID imposed.  cJ  K * (892) 0 K * (892) 0   (2S) →  +  - K + K -

14. Accepted by Phys. Rev. D, hep-ex/0408012 K * (892) significance = 4.7σ, 4.5σ, 7.6σ  c0  c1  c2

15. f 0 (980) controversial: Even mass and width complicated by KK threshold. Experimental results needed. Study  (2S) →  χ c0 →  f 0 f 0 →  +  -  +  - Require Prob(  2 4c ) > 1%. qq-bar meson? KK-bar molecule? multiquark state? glueball ?  c0  f 0 (980)f 0 (980)

16.  c0 →  +  -  +  -  c2 →  +  -  +  - f0f0f0f0

17. Results N = 65 – 51/1.75 = 35.9 ± 9.0 significance = 4.6σ ε = (3.92 ± 0.07)% B(  (2S) →  c0 →  f 0 f 0 →  +  -  +  - ) = (6.5 ± 1.6 ± 1.3) x 10 -5 B(  c0 → f 0 f 0 →  +  -  +  - ) = (7.6 ± 1.9 ± 1.6) x 10 -4 f0f0 Accepted by PRD, hep-ex/0406079 Plot mass recoiling from f 0 (980)

18. In general, it is believed that  (2S)   cJ is dominated by the E1 transition, but with some M2 (for  c1 and  c2 ) and E3 contributions (for  c2 ). The calculated pure E1 transition rates and the experimental results are quite different. Determine the contributions of the higher multipoles S- and D-wave mixing of  (2S) and  (3770) may be the key to solve the long-standing  puzzle and to explain  (3770) non-DD decays. Crystal Ball studied the decay angular distributions in  (2S)   c2 using  (2S)    J/  first; no significant higher multipoles found (with limited statistics).  c2 polarization in  (2S)   c2,  c2   +  -, K + K -

19. No background from  c1 since the  c1   +  -, K + K - processes are forbidden by parity conservation.

20. The helicity amplitudes are determined by a maximum likelihood fit to the angular distribution, where x=A 1 /A 0, y=A 2 /A 0, A 0,1,2 are the  c2 helicity amplitudes.

21. good agreement is observed in all angular distributions  +  - K+K-K+K- combine them, quadrapole amplitude a 2 ´ octupole amplitude a 3 ´ consistent with the pure E1 transition well  : correlation factor (CB) Accepted by PRD, hep-ex/0409034

22.  c decays to pp, , h + h - KsKs, K *0 K *0 and f 0 (980)f 0 (980) are measured for the first time or with higher sensitivity using BESII’s 14 million  (2S) data sample. helpful to better understand the nature of  c states and test the new QCD approach. The helicity amplitudes of  (2S)   c2 are measured for  c2   +  - and K + K -, and x = 2.08  0.44, y = 3.03  0.66 with correlation  = 0.92 are obtained. in good agreement with a pure E1 transition More experimental facts are desired Theoretical predictions… SUMMARY   

23. Thank you 谢谢