1. Manifestation of intermediate meson loop effects in charmonium decays
Institute of High Energy Physics, CAS
Manifestation of intermediate meson loop effects in charmonium decays
Qiang Zhao
Institute of High Energy Physics, CAS
and Theoretical Physics Center for Science Facilities (TPCSF), CAS
The 5-th International Conference on Quarks and Nuclear Physics, Beijing, Sept. 22, 2009

2. Motivations
Charmonium decays as a probe for non-perturbative QCD mechanisms
Several exisiting puzzles in low-lying vector charmonium decays

3. Several well-known puzzles in charmonium decays
(3770) non-DD decay
“ puzzle” in J/,   VP decay
M1 transition problem in J/,    c, ( c)
Isospin-violating decay of  J/ 0, and  hc0
… …
Conjecture: These puzzles could be related to non-pQCD mechanisms in charmonium decays due to intermediate D meson loops.

4. Charmonium spectrum

5. Open-charm effects in charmonium decays
”(3770)
DD threshold
’(3686)
Mass (MeV)
c(2980) 
J/(3096)
c(2980)
OZI rule violating transition
Light mesons
, , K*K, …
The open DD threshold is close to (3686) and (3770), which suggests that these two states will experience or suffer the most from the open channel effects.
Nevertheless, such effects behave differently in the kinematics below or above the threshold.
0 (L=0,S=0)
1 (L=0,S=1)
1 (L=2,S=1)

6. (3770) non-DD decay
-- Evidence for intermediate D meson contributions to charmonium decays

7. Particle Data Group 2008

8. Particle Data Group 2008

9. Particle Data Group 2008

10. (3770) non-DD decay Experimental discrepancies:
Exclusive DD cross sections are measured at BES and CLEO-c:

11. The lower bound suggests the maximum of non-DD b.r. is about 6.8%.
BES-II: non-DD branching ratio can be up to 15%
CLEO-c:
The lower bound suggests the maximum of non-DD b.r. is about 6.8%.

12. Inclusive non-DD hadronic cross sections from BES

13. Theoretical discrepancies:
In theory

14. pQCD calculation: BR(non-DD) < 5%
Short-range pQCD transition;
Color-octet contributions are included;
2S-1D state mixings are small;
NLO correction is the same order of magnitude as LO.
Results do not favor both CLEO and BES
NNLO ?
pQCD calculation: BR(non-DD) < 5%
Q: How about the long-range non-pQCD mechanisms?

15. Recognition of possible long-range transition mechanisms
pQCD (non-relativistic QCD):
If the heavy cc are good constituent degrees of freedom, c and c annihilate at the origin of the (cc) wavefunction. Thus, NRQCD should be valid.
pQCD is dominant in (3770)  light hadrons via 3g exchange, hence the OZI rule will be respected.
 (3770) non-DD decay will be suppressed.
Non-pQCD:
Are the constituent cc good degrees of freedom for (3770)  light hadrons? Or is pQCD dominant at all?
If not, how the OZI rule is violated?
Could the OZI-rule violation led to sizeable (3770) non-DD decay?
How to quantify it?

16. Recognition of long-range transition mechanisms
in spectrum studies
Hadronic loop contributions as unquenched effects in charmonium spectrum
See talk by E. Swanson at Charmed Exotics, Bad Honnef, Germany
and T. Barnes and E. Swanson, PRC77, (2008)
Li, Meng and Chao, PRD80, (2009)

17. Recognition of long-range transition mechanisms
in (3770) non-DD decays
Short-range pQCD transition via single OZI (SOZI) process
Long-range OZI evading transition g M1 c M1
(3770)
(3770) c* M2 M2

18. (3770) decays to vector and pseudoscalar via DD and DD. + c. c
(3770) decays to vector and pseudoscalar via DD and DD* + c.c. rescatterings
Y.-J. Zhang, G. Li and Q. Zhao, Phys. Rev. Lett. 102, (2009)

19. Long-range non-pQCD amp.
The V  VP transition has only one single coupling of anti-symmetric tensor form
Transition amplitude can thus be decomposed as:
Long-range non-pQCD amp.
Short-range pQCD amp.

20. Effective Lagrangians for meson couplings
Coupling constants:

21. i) Determine long-range parameter in (3770)  J/ .
Soft  production
- mixing is considered
a form factor is needed to kill the loop integral divergence
The cut-off energy for the divergent meson loop integral can be determined by data, and then extended to other processes.

22. ii) Determine short-range parameter combing (3770)   and (3770)  .
Relative strengths among pQCD transition amplitudes:

23. iii) Predictions for (3770)  VP.

24. X. Liu, B. Zhang and X.Q. Li, PLB675, 441(2009)

25. Remarks
The t-channel transition is much more important than the s channel.
The s-channel can be compared with Rosner’s (2S)-(1D) mixing.
The only sizeable s channel is in (3770)  J/. It adds to the t-channel amplitude constructive. In contrast, the isospin-violating (3770)  J/0 experiences a destructive interference between the s and t channel.
There exists a strong correlation between the SOZI parameter gS and phase angle .
It is essential to have precise measurement of all the VP channels, i.e. , K*K+c.c. etc.

26. More evidences are needed …
In most cases, the estimate of loop contributions will suffer from cut-off uncertainties. Thus, one should look for systematic constraints on the model uncertainties in all relevant processes. …

27. Coherent study of the (3686)  VP is needed
Coherent study of the (3686)  VP is needed. In particular, It is important to investigate the meson loop effects in the problems of e.g. “ puzzle”, J/ and (3686) radiative decay. [see e.g. Zhao, Li and Chang, PLB645, 173(2007); Li, Zhao, and Chang, JPG (2008); Zhao, Li and Chang, arXiv: [hep-ph], and work in progress]
The relevant isospin-violating channels as a correlation with the OZI-rule violation (OZI-rule evading) process, e.g.   J/ 0. [Guo, Hanhart, and Meissner, arXiv: , PRL2009]
An analogue to the (3770) non-DD decay: the (1020) non-KK decay [see Li, Zhao and Zou, PRD77, (2008); Li, Zhang and Zhao, JPG36, (2009)]. ……

28. “ puzzle” and “12% rule”

29. Large “12% rule” violation in  !
“ puzzle” and “12% rule”
pQCD expectation of the ratio between J/ and ' annihilation:
“ puzzle”
R() =
 0.2 %
Large “12% rule” violation in  ! g c c *
JPC = 1
J/, '
J/, ' c* c*

30. Theoretical explanations: 1. J/   is enhanced
J/-glueball mixing:
Freund and Nambu, Hou and Soni, Brodsky, Lepage and Tuan
Final state interaction:
Li, Bugg and Zou
Intrinsic charmonium component within light vectors:
Brodsky and Karliner, Feldman and Kroll
2. '   is suppressed
Karl and Roberts: sequential fragmentation model
Pinsky: hindered M1 transition model
Chaichian and Tornqvist: exponential form factor model
Chen and Braaten: color octet Fock state dominance in J/
Rosner: ' and " mixing
Suzuki: possible hadronic excess in (2S) decay
3. Others …
Recent review by Yuan et al.

31. Branching ratios for J/ (cc)  V P
Same order of magnitude !
What accounts for such a large isospin violation?
Implications of the “ puzzle” …

32. Branching ratios for  V P
Particle Data Group
Comparable !?

33. +/ EM + Long-range int.   3g 3g
+/ EM + Long-range int.
“12% rule” will not hold if EM, and/or other possible transitions are important. g V V c c *
J/
J/ c* P c* P

34. The property of antisymmetric VVP coupling suggests that one can investigate the origin of the “ puzzle” between the strong and EM transitions.
The EM transition can be investigated by vector meson dominance (VMD) model.
The strong transition amplitude contributes to both isospin-conserved and isospin-violated transitions.

35. EM transitions in VMD VP coupling: V* coupling:
Transition amplitude:

36. I. Determine gVP in V   P

37. II. Determine e/fV in V  e+ e-* V e-

38. III. Determine gP in P  
IV. Form factors
Corrections to the V*P vertices:
All the relevant data are available !

39. V. Isospin-violated channel
We determine the cut-off energy  in the form factor by fitting the experimental branching ratios for the isospin-violating J/ and  decays.
By taking the branching ratio fractions, it shows that the 12% rule is approximately satisfied.
Rth(%) Rexp(%)
 parameter is determined by assuming the dominance of EM transition in isospin-violated channels. It should be refitted when strong isospin violation is included.

40. Parameterize the strong decay transition
Fig. (a): Contributions from short-range interactions
Fig. (b): Contributions from long-range interactions with the double OZI-rule violation
Possible glueball components inside I=0 mesons
Short-range dominant, single OZI process
Long-range dominant, double OZI process

41. Parameterized strong decay amplitudes:
reflects the strong decay coupling strength.
Form factor to take into account hadron size effects:
with

42. Fitting results including EM transitions
Zhao, Li and Chang, PLB645, 173(2007)
Li, Zhao, and Chang, JPG (2008)

43. Branching ratio fraction “R” including EM and strong transitions
Zhao, Li and Chang, PLB645, 173(2007), Li, Zhao, and Chang, JPG (2008)

44. Mechanisms suppressing the   VP strong decays should be clarified!
Unanswered questions
What is the origin of the strong coupling suppression on the   VP?
What is the role played by long-range interactions?
What is the correlation between the long-range interaction with the OZI-rule-evading mechanisms?
Mechanisms suppressing the   VP strong decays should be clarified!

45. 0 Mechanism suppressing the strong decay amplitudes of   VP
Open-charm effects as an OZI-rule evading mechanism D 
J/ () c D* 0 c D
Interferences among the single OZI, EM and intermediate meson loop transitions are unavoidable.

46. Decomposition of OZI evading long-range loop transitions
J/ ()  D  D 
J/ ()
J/ ()  V 
 … D* D  
t-channel
s-channel
Zhang, Li and Zhao, [hep-ph]; Li and Zhao, PLB670, 55(2008)

47. Recognition of interferences
Property of the anti-symmetric tensor coupling allows a parametrization:
In order to account for the “ puzzle”, a destructive phase between
and
is favored.
Zhao, Li, and Chang, [hep-ph].

48. Not include sign.

49. Some features about the open charm
The intermediate meson loops will contribute to the real part of the couplings since both J/ and  are below the open charm threshold.
Since the  has a mass which is closer to the open DD threshold, its amplitude via the DD loop will be qualitatively larger than J/ due to near-threshold effects.
Similar behavior due to intermediate DD(D*) and DD*(D) loops also shows up in a coherent study of J/ and  c and   c. (Li & Zhao, PLB670, 55(2008))
Light intermediate meson loops are strongly suppressed due to large off-shell effects.

50. Summary
Open DD channel effects seems to be essential for understanding some of the puzzles in the low-lying charmonium decays.
(3770) non-DD decays
“ puzzle” in J/, ’  VP
M1 transition problem in J/,    c, ( c)
Isospin violating decay of  J/0
However, the quantitative calculations are sensitive to cut-off energy and exhibit model-dependent aspects.
Systematic examinations of such a mechanism in different circumstances are necessary.
Experimental data from BES, CLEO-c, KLOE, and B-factories will further clarify those issues.

51. Thanks !

52. Puzzles in J/,    c, ( c)
-- Further evidence for intermediate D meson contributions to the M1 transitions

53. M1 transition in a naïve quark model
c 
c 
J/ c
c 
c 
M1 transition flips the quark spin
The initial and final qq states are in the same multiplet
The initial and final qq states have the same spatial wavefunction

54. Relativistic corrections, e.g. finite size corrections
M1 transition in the relativised Godfrey-Isgur model
Relativistic corrections, e.g. finite size corrections
Form of long-rang force is unknown
Sensitivities to the quark masses and details of the potential
   c is also allowed (hindered transition)

55. NRQCD, higher-order corrections, relativistic quark model, Lattice QCD…
Relativistic quark model, Ebert et al. :
predictions are sensitivity to Lorentz structure of the quark potentials

56.  Tree level effective Lagrangian c J/
In terms of effective coupling, the correction is to the VVP coupling form factors.

57. Intermediate meson exchange with effective Lagrangians

59. Vertex couplings are determined by available experi. Info.

60. Contact diagrams
with

61. Results and discussions
Overall transition amplitude:   D D*
J/ c
J/ D c

62. Small imaginary amplitudes
The real part is supposed to cancel the M1 amplitude
Simultaneous account of the J/,   c with the same cut-off energy 
Prediction for   c