1. Fact and fancy – on the “ puzzle”
Institute of High Energy Physics, CAS
Fact and fancy
– on the “ puzzle”
Qiang Zhao
Institute of High Energy Physics, CAS
and Theoretical Physics Center for Science Facilities (TPCSF), CAS
Symposium on the “12% rule” and “rho-pi puzzle”, Mar , 2011, Beijing

2. Outline 1. QCD says … 2. Experimental facts 3. Fancy theories
4. Missing pieces of the jigsaw puzzle?

3. 1. pQCD says something

4. 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

5. 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!

6. pQCD expectation of the ratio between J/ and ' annihilation:
Short-distance dominant – “12% rule”
pQCD expectation of the ratio between J/ and ' annihilation: g c c *
JPC = 1
J/, '
J/, ' c* c*

7. 2. Experimental facts

8. Large “12% rule” violation in  !
“ puzzle”
R() =
 0.2 % g  c c  *
J/, '
J/, '  c*  c*
Large “12% rule” violation in  !

9. Branching ratios for J/ (cc)  V P
More than “” … …
Branching ratios for J/ (cc)  V P
Same order of magnitude !

10. Branching ratios for  V P
Particle Data Group
Comparable !?
What accounts for such a large isospin violation?
Correlation between the helicity selection rule and OZI rule violations
Implications of the “ puzzle” …

11. 3. Fancy theories

12. Theoretical explanations:
1. J/   is enhanced
J/-glueball mixing:
Freund and Nambu, Hou and Soni, Brodsky, Lepage and Tuan
Assuming a general validity of the pQCD hadron helicity theorem
Final state interaction:
Li, Bugg and Zou (light meson loops)
Intrinsic charmonium component within light vectors:
Brodsky and Karliner, Feldman and Kroll
Mechanisms for evading the helicity selection rule

13. 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 due to intermediate DD
… …
Yuan, Wang, Mo, CPC2008
X.Q. Li, CPC2010

14.   Natural and unnatural …
+/ EM + Long-range int.   3g 3g
+/ EM + Long-range int.
Helicity selection rule violating
“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

15. The isospin-violating decay channels also fit in “12%” rule?
Rth(%) Rexp(%) V c *
J/ c* P

16. 4. Missing pieces of the jigsaw puzzle?

17. You may “see” something nice here, but you need to crack down it …

18. We still need to work hard to put every pieces together …

20. Scattered pieces of the jigsaw puzzle ?
“ puzzle” in J/,   VP decay
(3770) non-DD decay
M1 transition problem in J/,    c, ( c)
Recent puzzling results for J/,    ,  
Large c  VV branching ratios
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.

21. (3770) non-DD decay
-- IML as a mechanism for evading the helicity selection rule

22. 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]

23. 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.
Ref: He, Fan and Chao, PRL101, (2008)

24. 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%
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 ?

25. 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?

26. (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 

27. (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)

28. 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.

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

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

31. “ puzzle” and “12% rule”

32. Mechanism suppressing the strong decay amplitudes of   VP
Open-charm effects as an OZI-rule evading mechanism D
J/ () V
J/ () g V c c D* c P c* P D
SOZI: pQCD dominant
OZI-evading: non-pQCD dominant
Interferences among the single OZI, EM and intermediate meson loop transitions are unavoidable.

33. 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)

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

35. Not include sign.

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

37. To firm up open charm effects …
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
(refs.: T. Barnes and E. Swanson, PRC77, (2008); Li, Meng and Chao, PRD80, (2009)
3) Compare different theoretical approaches, e.g. NREFT and ELA in isospin-violating charmonium decays.
(refs.: Guo, Hanhart, and Meissner, PRL(2009); Guo, Hanhart, Li, Meissner, QZ, PRD(2010); and PRD(2011).)

38. To pin down the underlying dynamics
Direct test of rho-pi puzzle:
J/,  PP for the role played by EM annihilations (X.Q. Li)
c, c  VV for the role played by strong annihilations (Wang, Liu, QZ)
Indirect tests:
Helicity selection rule violation processes and correlations with the OZI rule violations (Liu et al; Liu, Wang, QZ)
Strong isospin violations via charmed meson loops (Guo, Hanhart, Li, Meissner, QZ)
Open charm effects in the cross section lineshape studies
B meson loops in Upsilon decays (Chao et al)
Open threshold effects on the charmed meson spectrum (Barnes et al; Chao and Meng)

39. Open charm effects in the cross section lineshape studies
X(3900) ?
(3770)
(4040)
(4160)
(4415)
e+e-  DD
What is X(3900)?
Not inlcuded in PDG2010.
Not in charmonium spectrum
… …
Pakhlova et al., PRD77, (2008).

40. Direct evidence for open charm effects in the cross section lineshape studies
Wang, Liu, QZ, [hep-ph]

41. Thanks ! More theory studies … … More Experimental measurements … …
Let the “fact” tell us the “fancy” part of the world … …
Thanks !

42. References: Q. Zhao, Phys. Lett. B697, 52 (2011).
Q. Wang, X.-H. Liu and Q. Zhao, arXiv: [hep-ph].
F.-K. Guo, C. Hanhart, G. Li, Ulf-G. Meißner, Q. Zhao, Phys. Rev. D83, (2011); arXiv: [hep-ph].
X.-H. Liu and Q. Zhao, J. Phys. G 38, (2011); 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)