1. Effects of charmed meson loops on charmonium transitions
Institute of High Energy Physics, CAS
Effects of charmed meson loops on charmonium transitions
Qiang Zhao
Institute of High Energy Physics, CAS
and Theoretical Physics Center for Science Facilities (TPCSF), CAS
The 4th International Conference on Charm Physics – Charm 2010, Oct , 2010, Beijing

2. Motivations
Charmonium decays as a probe for non-perturbative QCD mechanisms, e.g. OZI rule evasion transitions.
pQCD helicity selection rule is badly violated in exclusive processes.
There exist several 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
Large c  VV branching ratios
M1 transition problem in J/,    c, ( c)
Isospin-violating decay of  J/ 0, and  hc0
Could be 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. Observations

5. Helicity selection rule
According to the perturbative method of QCD, Chernyark and Zitnitsky showed that the asymptotic behavior for some exclusive processes has a power-counting as follows:
Chernyark and Zitnitsky, Phys. Rept. 112, 173 (1984); Brodsky and Lepage, PRD24, 2848 (1981).
The QCD leading term will contribute when 1+2=0, while the next to leading order contribution will be suppressed by a factor of 2QCD/mc2

6. S- and P-wave charmonium exclusive decays
“-” : forbidden by angular-momentum and parity conserv.
“ε” : to leading twist order forbidden in pQCD
“” : to leading twist order allowed in pQCD
“()” : either G-parity or isospin are violated
(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!

7. 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*

8. Contradictions in exp. observations: (3770)
(3770) non-DD decays g c
Contradictions in exp. observations:
(3770)
Non-DD c
BES-II:
Up to 15 %
CLEO-c:
< 9 % at 90% C.L.
Updated results from CLEO-c : [hep-ex]

9. Contradictions in pQCD calculations：
NRQCD leading order calculations gave negligible contributions from the (3770) non-DD decays.
Refs: Kuang and Yan, PRD41, 155 (1990); Ding, Qin and Chao, PRD44, 3562 (1991); Rosner, PRD64, (2001)
However, calculations including NLO yield significant corrections, which can account for up to 5% branching ratios.
Ref: He, Fan and Chao, PRL101, (2008)
Questions:
1) Would QCD perturbative expansion still be valid in the charmonium energy region?
2) Would other non-perturbative mechanisms play a role in (3770)  non-DD ?

10. (3770) (3770) D(cq) (ud) D c c D D(qc) (du) DD thresh.
The (3686) and (3770) will experience or suffer the most from the DD open channel effects. Such effects behave differently in the kinematics below or above the threshold.
(3770)
(3770)
D(cq)
(ud)
(3770) non-DD decays D c c
Mass c c D
D(qc)
(3770)
(du)
DD thresh.
(3686)
(ud) D c
J/(3096) c
“ puzzle” D
(3686)
(du)
JPC = 1 

11. (3770) non-DD decay
-- IML as a mechanism for evading the helicity selection rule

12. (3770) hadronic decays via intermediate D meson loops
Quantitative study of (3770)  VP is possible.
Y.-J. Zhang, G. Li and Q. Zhao, PRL102, (2009)

13. 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.

14. Effective Lagrangians for meson couplings
Coupling constants:
Cacalbuoni et al, Phys. Rept. (1997).

15. 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.

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

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

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

19. 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.
Look for effects of hadronic loop contributions as unquenched effects in charmonium spectrum
(T. Barnes and E. Swanson, PRC77, (2008); Li, Meng and Chao, PRD80, (2009)
3) Compare different theoretical approaches, e.g. in isospin-violating charmonium decays.
(See talk by Ulf-G. Meissner; Guo, Hanhart, and Meissner, PRL(2009); Guo, Hanhart, Li, Meissner, QZ, PRD(2010); and [hep-ph])

20. -- a cross check between NREFT and ELA
Study of charmed meson loops in charmonium hadronic transitions with a single 0 or  emission
-- a cross check between NREFT and ELA
Ref. Guo, Hanhart, Li, Meissner, and Zhao, arXiv: [hep-ph]

21. Slide from Ulf-G. Meissner

22. Comparisons between NREFT and ELA in charmonium decays

25. Summary-1
Open charmed meson channel effects seems to be essential for understanding some of those long-standing puzzles in charmonium decays into light hadrons.
(3770) non-DD decays
“ puzzle” in J/, ’  VP
M1 transition problem in J/,    c, ( c)
Isospin violating decay of  J/0
… …
It also provides a possible mechanism for the helicity selection rule violations observed in charmonium decays.
Helicity selection violating channels:   VP, c1  VV, c2  VP, c(c) VV …

26. Summary-2
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 BESIII, CLEO-c, KLOE, and B-factories will further clarify those issues.

27. References:
Q. Wang, X.-H. Liu and Q. Zhao, arXiv: [hep-ph].
F.-K. Guo, C. Hanhart, G. Li, Ulf-G. Meißner, Q. Zhao, arXiv: [hep-ph].
X.-H. Liu and Q. Zhao, arXiv: [hep-ph].
F.-K. Guo, C. Hanhart, G. Li, Ulf-G. Meißner, Q. Zhao, Phys. Rev. D 82, (2010); arXiv: [hep-ph].
X.-H. Liu and Q. Zhao, Phys. Rev. D 81, (2010)
Y.J. Zhang, G. Li and Q. Zhao, Phys. Rev. Lett. 102, (2009); arXiv: [hep-ph].
Q. Zhao, G. Li and C.H. Chang, Chinese Phys. C 34, 299 (2010);
G. Li and Q. Zhao, Phys. Lett. B 670, 55(2008).
G. Li, Q. Zhao and C.H. Chang, J. Phys. G 35, (2008)
Q. Zhao, G. Li and C.H. Chang, Phys. Lett. B 645, 173 (2007)
Thanks !

28. “ puzzle” and “12% rule”
Spare slides
“ puzzle” and “12% rule”

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

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

31. +/ 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

32. V. Isospin-violated channel
Cut-off energy  is determined by fitting the experimental branching ratios for the isospin-violating J/ and  decays.
The approximate respect of the 12% rule suggests a single transition mechanism via EM process.
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.

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

34. 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!

35. 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.

36. 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)

37. 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].

38. Not include sign.