Qiang Zhao Institute of High Energy Physics, CAS and Theoretical Physics Center for Science Facilities (TPCSF), CAS A coherent view of the charmonium hadronic and radiative decays Institute of High Energy Physics, CAS 474th International Wilhelm und Else Heraeus Seminar, “Strong Interaction: From Methods to Structures”, Feb. 15, 2011, Bad Honnef, Germany

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.

 (3770) non-D  D decay “  puzzle” in J/ ,   VP 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   h c  0 Could be more … … Conjecture: 1)These puzzles could be related to non-pQCD mechanisms in charmonium decays due to intermediate D meson loops. 2)The intermediate meson loop transition could be a mechanism for the evasion of the helicity selection rule. Several well-known puzzles in charmonium decays

Observations Observations

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: The QCD leading term will contribute when =0, while the next to leading order contribution will be suppressed by a factor of   QCD /m c 2 Chernyark and Zitnitsky, Phys. Rept. 112, 173 (1984); Brodsky and Lepage, PRD24, 2848 (1981).

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

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

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

 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)

 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 ?

 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?

J/  (3096)  (3686)  (3770) D  D thresh. Mass J PC = 1   c cc  (3770) D(c  q)  D(q  c)  (3686) c cc (ud)(ud) (du)(du) 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. D DD “  puzzle”  (3770) non-D  D decays  (3770) c cc (ud)(ud) (du)(du) D DD

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

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

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

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

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

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

iii) Predictions for  (3770)  VP.

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

“  puzzle” and “12% rule” “  puzzle” and “12% rule”

pQCD expectation of the ratio between J/  and  ' annihilation: “  puzzle” R(  ) = c J/ ,  ' g c c* ** J/ ,  ' c* J PC = 1   0.2 %  “  puzzle” and “12% rule”

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

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

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

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

Not include sign.

1)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. 2)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).) More evidences are needed …

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, PRD(2011); See talk by F.-K. Guo.

Power-counting rules for charmed meson loops q: momentum of the final state  /   : isospin/SU(3) symmetry breaking strength v: heavy quark velocity, ~ 0.5  : charmed meson mass difference

Comparisons between NREFT and ELA in charmonium decays

Qualitatively agree!

Quantitatively agree!

 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 …

 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 and comparisons between different approaches (e.g. NREFT and ELA) are necessary. Experimental data from BESIII, CLEO-c, KLOE, and B- factories will further clarify those issues.

References: 1.Q. Zhao, Phys. Lett. B697, 52 (2011). 2.Q. Wang, X.-H. Liu and Q. Zhao, arXiv: [hep-ph]. 3.F.-K. Guo, C. Hanhart, G. Li, Ulf-G. Meißner, Q. Zhao, Phys. Rev. D83, (2011); arXiv: [hep-ph]. 4.X.-H. Liu and Q. Zhao, J. Phys. G 38, (2011); arXiv: [hep-ph]. 5.F.-K. Guo, C. Hanhart, G. Li, Ulf-G. Meißner, Q. Zhao, Phys. Rev. D 82, (2010); arXiv: [hep-ph]. 6.X.-H. Liu and Q. Zhao, Phys. Rev. D 81, (2010) 7.Y.J. Zhang, G. Li and Q. Zhao, Phys. Rev. Lett. 102, (2009); arXiv: [hep-ph]. 8.Q. Zhao, G. Li and C.H. Chang, Chinese Phys. C 34, 299 (2010); 9.G. Li and Q. Zhao, Phys. Lett. B 670, 55(2008). 10.G. Li, Q. Zhao and C.H. Chang, J. Phys. G 35, (2008) 11.Q. Zhao, G. Li and C.H. Chang, Phys. Lett. B 645, 173 (2007) Thanks !

(I) Charmonium radiative decays into light pseudoscalars (I) Charmonium radiative decays into light pseudoscalars Backup slides

,  c cc J/    A probe of strong QCD dynamics Glue-rich intermediate states Dynamics for Okubo-Zweig-Iizuka (OZI) rule violation Probe the structure of pseudoscalars, e.g.  -  mixing Search for exotics, e.g. glueballs … … G

 Feldmann-Kroll-Stech’s  -  mixing scheme In the quark flavor basis: where  q = (u  u + d  d)/  2,  s = s  s, and FKS ansatz: The decay constants share the same mixing angles in the quark flavor basis. Feldmann, Kroll and Stech, PRD58, (1998)

FKS ansatz is a consequence of SU(3) flavor symmetry breaking, which requires a single choice of the basis states. Nevertheless, the matrix of the decay constants follows the particle state mixing, and the decay constants of the mesons are mass independent superpositions of f q and f s. Axial vector anomaly gives:

The ratio of couplings of our basis states to the anomaly: Anomaly contributions to the mass matrix:

 Generalize to  -  -  c mixing scheme Feldmann, Kroll and Stech, PRD58, (1998) c cc q qq

,  c cc J/   In the J/  radiative decays, the photon is radiated by c quarks, and then cc-bar annihilate into light quark pairs via the anomaly effects: It implies a mixing of  -  -  c via the axial gluonic anomaly in J/  radiative decays. In particular, the anomaly effects saturate the decay branching ratios!

,  c cc J/   cc  ,  cc J/  Anomaly saturated decays: Implications: The decays are dominated by the  c pole contributions. Mixings among  -  -  c are calculable. Novikov, Shifman, Vainshtein, and Zakharov, NPB165, 55 (1980) K.T. Chao, NPB335, 101 (1990) Feldmann, Kroll and Stech, PRD58, (1998)

 ,  cc J/   ()  c Calculations of K.T. Chao, NPB335, 101 (1990) BR(J/    c ) = (1.7  0.4) %

Questions: How about if the anomaly does not saturate the decay branching ratios? What would be other contribution mechanisms? What is the evidence? CLEO, PRD79, (2009) BESIII, PRL105, (2010); [hep-ex] Puzzling data for J/  and    P:

 Vector meson dominance (VMD) in charmonium radiative decays ,  c cc J/    The photon is produced via couplings to vector meson resonances. Pseudoscalars are produced by soft gluon radiations. The charm quarks annihilate in a relative S-wave and spin-1 configuration at short distances. The VMD processes do not overlap with the anomaly transitions.

 VMD model V  * coupling: V ** e+ e-

where the on-shell parameter g  VP is determined by   VP: with the form factor: Transition amplitude given by VMD model  = 300 MeV.

Considered VP channels

Effective couplings extracted from exp. data:

The VMD contributions are generally given by the intermediate charmonium states. Contributions from light VP channels are generally small. The anomaly contributions are dominant in J/  decays, but not in . VMD contributions seem to be important in charmonium radiative decays, but have never been addressed before.  Separated contributions from VMD and anomly via  c mixings:

 Coherent results including both VMD and anomly effects via  c mixings fit the branching ratio patterns quite well.

A prediction for  (3770): The anomaly contributions in  (3770) is small due to the suppressions on the M1 transitions between different main quantum numbers. In contrast, the decay of  (3770)  J/   has been observed.

Brief Summary Charmonium radiative decay into light pseudoscalars is an ideal process for understanding the pseudoscalar meson production mechanisms. The axial gluonic anomaly is dominant in J/    P, but not in    P. For the latter, the VMD appears to be more important. The VMD mechanism is a novel phenomenon in charmonium radiative decays.