1. Decay of P wave triplet cJ
Wang Zhiyong
Summer school
Jun ,2008

2. Outline Introduction Transition decay Two-body decay
Pseudoscalar pair
Vector pair
Baryon pair
multi-body decay & PWA
Three-body
Four-body
Summary

3. Low-lying Charmonium Family
What I will talk about

4. Overview on current status
The summation of the all available measured BR for cJ decay channels from PDG are
Here B(c1J/)=(35.61.9)% and B(c2J/)=(20.21.0)% , i.e. most decay modes of cJ are still unknown.

5. Why most decay modes of cJ are unknown?
Similar to J/, the decay of cJ is OZI-suppressed or DOZI-suppressed except transition decay. No extremely large branching ratio can be found in cJ decay. The two largest branching ratios are
The small data sample. Limited by JPC, the large cJ data sample can not be available via e+e collision, but obtained from (2S) transition decay.

6. transition decay c0,1,2J/
Purpose: Search for the evidence from high-order transition(above E1 model)

7. Transition decay Here B is the helicity amplitude
If pure E1 transition, then
For cJ J/, there is the similar expression, but helicity amplitude is A

8. Transition decay For the cascade decay of cJ ，cJ J/J
Where 1 is the angle between the first radiative photon and the beam direction. (2,) are the polar angles of the second radiative photon measured in the cJ rest frame. n runs over integer values from zero to at most s. a, b,c and d are some parameters concerning helicity amplitude.
For 1 ，1 J/J
Where x=|B1/B0| and y=|B2/B0| , B=22 -1,=|A0/A1|
For 2 ，
2 J/J
Where x and y are same as above. =62+2 -4,H=2-22, =A0/A1, =A2/A1

9. Transition decay
What we focus on is the multipole amplitudes aJ in c1,2 J/ and bJ in c1,2. The relation between aJ, bJ and A, B is
If a1,b1 are far away from 1 and a2,b2,a3, b3 are far from 0, it indicates that there are obvious contributions from high-order transition
For J=0
a1,b1E1
a2,b2M2
a3,b3E3
For J=1
For J=2
Similar expression for B’s

10. Study status of transition decay
c0,1,2J/, They are measured via
E  high,
not single
Two-body decay
Only the branching ratios are measured now!
No obvious c0 signal
E low, single
(E= 273,175,130 MeV)
c1
c2
BESII result
CLEO result

11. Transition decay
The study on transition decay require that the candidate sample has
High statistics
Negligible background
Large polar angle cover
It is possible to carry out this study in BESIII
Large BR for this transition decay.
Background from (2S)00 J/ is suppressed very much!
cos = 0.93 in BESIII.

12. Two-body decay
PP pseudoscalar pair
VV vector pair
BB baryon pair

13. Motivation The study of cJSS,PP,VV can be used to
Understand the contribution from high-order process.
Clarify the role played by the OZI-rule violations.
Disentangle the correlations from different mechanisms in the charmonium decays into light hadrons. 
The measurement of cJBB can be used to
Test the color-octet state theory.
Q. Zhao, PRD 72(2005) )
S.M. Wang, Eur. Phys. J. C 14,643(2000)

14. cJPP c0,2+,00, K+K,KsKs, ,  c0,1,2 
Note: c1 PP is suppressed if P is the identical particle.

15. BES results(c0,200,,KsKs) Measurement precisions are very low!
BES-I
BES-I
BES-II
Measurement precisions are very low!

16. BES results (c0,2+,K+K)
The current result do not contradict E1 theoretical model

17. CLEO’s result
c0,2+, 00,K+K,KsKs,, ,  have been measured.
CLEO Preliminary!

18. Theory test
CLEO’S result suggest small if any contribution for DOZI decay in 0-+ channel!

19. The last two decay modes are not currently available
cJVV
, , K*0K*0, , K*+K*, .
The last two decay modes are not currently available

20. BES results(, , K*0K*0)_
BES results(, , K*0K*0) _
B(cJ,,K*0K*0) are measured with low precision at BES (PLB, 630 7, PLB, 642, 197, PRD 70, ). No measurement is currently available from CLEO about cJ VV mode.

21. BES results(, , K*0K*0)
Branching ratio of cJ , , K*0K*0(10-3)
cJ
Mode
c0
c1
c2 
2.29 0.580.41 --
1.770.470.36 
0.940.21  0.13
1.70
K*0K*0
1.780.34 0.34
1.670.32 0.31
4.860.56 0.88
The measurement precision are very low!

22. cJ
E low
E high

23. Statistical error is still dominant in CLEO’s measurement!
cJ
Statistical error is still dominant in CLEO’s measurement!

24. pp,,00,+, + 00,++- -,+_
cJ BB _ _ _ _ _
pp,,00,+, + 00,++- -,+ _ _ _

25. BES results (pp, +) BES’s measurement precisions are very low_ _
BES results (pp, +)  pp
+
BES’s measurement precisions are very low

26. BES results (pp, +) Branching ratio of cJ pp, , +–(10-4)_ _
BES results (pp, +)
Branching ratio of cJ pp, , +–(10-4)
cJ
Mode
c0
c1
c2 pp
2.71 0.430.47
0.570.17 0.09
0.650.24 0.10 
4.71.3 1.0
2.61.0 0.6
3.31.5 0.7
+–
5.32.7 0.9
<3.4
<3.7

27. _
cJ ++- -
BES-II results
(unpublished)
++  region
M++ 

28. CLEO’s results
First observation

29. CLEO’s results

30. cJ  Multi-body
h+hh0
4-body

31. BES results(cJ KsK++c.c, +)
a0(980)
K*(892)
K*(1430)
f2(1270)

32. CLEO’s results (3M sample) cJ K+K, +, pp, +
f2(1270)
a0(980)
cJ K+K, +, pp, +

33. cJ KsK++c.c.,K+K0,pp0,Kp
CLEO’s results
cJ KsK++c.c.,K+K0,pp0,Kp

34. CLEO’s results
cJ KsK+ + c.c.

35. cJ 4-body & partial wave analysis (PWA)

36. PWA of c0+-K+K(BES result)
(770)
f0(1710)
f0(980)
f0(1270)
f0(2200)
K*0(892)
K*0(1430)
K*0(1430)

37. PWA of c0+-K+K

38. PWA of c0+-K+K

39. cJ h+hKsKs (BES)

40. cJ h+hKsKs(BES)

41. cJ h+hh0h0
+00
K+K00
pp00
K+K
KKs 0

42. CLEO’s results

43. (770) is obvious in all 0 combinations
cJ  +00
(770) is obvious in all 0 combinations

44. cJKKs0
K*(892) is obvious in all K combinations and (770) is obvious in all 0 combinations

45. cJ h+hh0h0

46. Thank you! Summary Most decay modes of cJ are still unknown.
Most currently available measured precision of cJ decay are very poor except transition decay.
Transition decay and c0,2PP mode can be used to test E1 theory.
cJ VV (,,K*K*,,) + PP(,,,KK) can be used to clarify the role played by the OZI-rule violations.
c0,2BB can be used to test COM theory.
For the multi-body decay of cJ, intermediate states can be found in all modes. Partial Wave Analysis (PWA) is necessary if one want to obtain more details.
For cJ study, we should put our efforts along with two directions
depth (improve the current measured precision),
width (search new decay mode).
A large (2S) data sample is necessary !!!
Thank you! _