1. Revisiting some long-standing puzzles in charmonium decays
Institute of High Energy Physics, CAS
Revisiting some long-standing puzzles in charmonium decays
Qiang Zhao
Institute of High Energy Physics, CAS
and Theoretical Physics Center for Science Facilities (TPCSF), CAS
Contributors: G. Li, X.-H. Liu, and Y.-J. Zhang
3rd FCPPL Conference, Lyon, April 7-10, 2010

2. Motivations
Charmonium decays as a probe for non-perturbative QCD mechanisms
pQCD helicity selection rule is badly violated
Several exisiting puzzles in low-lying vector charmonium decays could be related with non-perturbative mechanisms.

3. Several well-known puzzles in charmonium decays
(3770) non-DD decay
“ puzzle” in J/,   VP decay
Large c  VV branching ratios
M1 transition problem in J/,    c, ( c)
Isospin-violating decay of  J/ 0, and  hc0
Even more … …
Conjecture:
These puzzles could be related to non-pQCD mechanisms in charmonium decays due to intermediate D meson loops.
The intermediate meson loop transition could be a mechanism for the evasion of the helicity selection rule.

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. Outline Introduction to the helicity selection rule
Long-distance contribution from intermediate meson loop (IML) transitions
(3770) non-DD decays
“ puzzle”
c1→VV, c2→VP, c, c0, hc BB (X.-H. Liu, talk in the satellite meeting)
Summary

7. Helicity selection rule
Base on the pQCD quark-gluon interaction, the asymptotic behavior of exclusive hadronic processes has a power-counting as follows:
Chernyark and Zitnitsky, Phys. Rept. 112, 173 (1984); Brodsky and Lepage, PRD24, 2848 (1981).
The QCD leading twist will contribute when 1+2=0, while the next to leading order contribution will be suppressed by a factor of 2QCD/mc2

8. Helicity selection rule
An alternative description of this selection rule with the quantum number named “naturalness”
The selection rule requires that
Take the process J/ VP as an example
In the rest frame of initial state, it requires V=0 at leading twist accuracy. V can be approximately expressed as a linear combination of the final state momenta, which then results in a vanishing amplitude.

9. S- and P-wave charmonium exclusive decays
(3770)
(3770) non-DD decays into VP
“ puzzle”-related
Feldmann and Kroll, PRD62, (2000)
PDG2008
The helicity selection rule seems to be violated badly in charmonium decays!

10. (3770) non-DD decay
-- IML as a mechanism for evading the helicity selection rule

11. Particle Data Group 2008

12. Particle Data Group 2008

13. Particle Data Group 2008

14. (3770) non-DD decay Experimental discrepancies:
Exclusive DD cross sections are measured at BES and CLEO-c:

15. 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%.

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

17. Theoretical discrepancies:
In theory

18. 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?

19. 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?

20. 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

21. (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)

22. 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.

23. Effective Lagrangians for meson couplings
Coupling constants:

24. 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.

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

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

27. 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.

28. More evidences for the meson loop contributions 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. …

29. 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)].
Helicity selection rule evasions in c1  VV and c2  VP. [see Liu and Zhao, PRD81, (2010)]
Helicity selection rule evasions in c, c0, hc BB. [ Liu and Zhao, arXiv: [hep-ph]. ]
Other cases where the helicity selection rule is violated.

30. Thanks !