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Qiang Zhao Institute of High Energy Physics, CAS

Institute of High Energy Physics, CAS. A coherent view of the charmonium hadronic and radiative decays. Qiang Zhao Institute of High Energy Physics, CAS and Theoretical Physics Center for Science Facilities (TPCSF), CAS zhaoq @ ihep.ac.cn.

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Qiang Zhao Institute of High Energy Physics, CAS

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

  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 • 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.

  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, 074006 (2000) PDG2008 The helicity selection rule seems to be violated badly in charmonium decays!

  7. “ 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. (3770) non-DD decays g c • Contradictions in exp. observations: Non-DD (3770) c Up to 15 % BES-II: CLEO-c: < 9 % at 90% C.L. Updated results from CLEO-c : 1004.1358[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, 094002 (2001) • However, calculations including NLO yield significant corrections. • Ref: He, Fan and Chao, PRL101, 112001 (2008)

  10. 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 ?

  11. 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?

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

  13. (3770) non-DD decay -- IML as a mechanism for evading the helicity selection rule

  14. (3770) hadronic decays via intermediate D meson loops Quantitative study of (3770)  VP is possible. Y.-J. Zhang, G. Li and Q. Zhao, PRL102, 172001 (2009)

  15. 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.

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

  17. i) Determine long-range parameter in (3770)  J/ . (3770) J/ (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.

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

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

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

  21. “ puzzle” and “12% rule”

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

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

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

  25. Decomposition of OZI evading long-range loop transitions D  J/ ()  D   D J/ () J/ () V    … D* D   t-channel s-channel Zhang, Li and Zhao, 0902.1300[hep-ph]; Li and Zhao, PLB670, 55(2008)

  26. 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, 0812.4092[hep-ph].

  27. Not include sign.

  28. 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 (refs.: T. Barnes and E. Swanson, PRC77, 055206 (2008); Li, Meng and Chao, PRD80, 014012(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).)

  29. 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.

  30. 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

  31. Comparisons between NREFT and ELA in charmonium decays

  32. Qualitatively agree!

  33. Quantitatively agree!

  34. 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 …

  35. 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.

  36. References: • Q. Zhao, Phys. Lett. B697, 52 (2011). • Q. Wang, X.-H. Liu and Q. Zhao, arXiv:1010.1343[hep-ph]. • F.-K. Guo, C. Hanhart, G. Li, Ulf-G. Meißner, Q. Zhao, Phys. Rev. D83, 034013 (2011); arXiv:1008.3632[hep-ph]. • X.-H. Liu and Q. Zhao, J. Phys. G 38, 035007 (2011); arXiv:1004.0496 [hep-ph]. • F.-K. Guo, C. Hanhart, G. Li, Ulf-G. Meißner, Q. Zhao,Phys. Rev. D 82, 034025 (2010); arXiv:1002.2712[hep-ph]. • X.-H. Liu and Q. Zhao, Phys. Rev. D 81, 014017 (2010) • Y.J. Zhang, G. Li and Q. Zhao, Phys. Rev. Lett. 102, 172001 (2009); arXiv:0902.1300 [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, 055002 (2008) • Q. Zhao, G. Li and C.H. Chang, Phys. Lett. B 645, 173 (2007) Thanks !

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

  38. A probe of strong QCD dynamics  c J/ G ,  c • 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 • … …

  39. 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, 114006 (1998)

  40. 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 fqand fs. Axial vector anomaly gives:

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

  42. Generalize to --c mixing scheme c q c q Feldmann, Kroll and Stech, PRD58, 114006 (1998)

  43. 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:  c J/ ,  c 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!

  44. Anomaly saturated decays:   c J/ J/ ,  c ,  c c • 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, 114006 (1998)

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

  46. Questions: • How about if the anomaly does not saturate the decay branching ratios? • What would be other contribution mechanisms? • What is the evidence? Puzzling data for J/ and    P: BESIII, PRL105, 261801(2010); 1011.0889[hep-ex] CLEO, PRD79, 111101 (2009)

  47. Vector meson dominance (VMD) in charmonium radiative decays  • 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.  c J/ c , 

  48. VMD model e+ * V e- V* coupling:

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

  50. Considered VP channels

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