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Qiang Zhao Theory Division Institute of High Energy Physics, CAS Email: zhaoq@ihep.ac

Univ. of Science and Technology of China June 22, 2007. Topics on charmonium hadronic decays. Qiang Zhao Theory Division Institute of High Energy Physics, CAS Email: zhaoq@ihep.ac.cn. Outline. Charm quark and charmonium spectrum

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Qiang Zhao Theory Division Institute of High Energy Physics, CAS Email: zhaoq@ihep.ac

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  1. Univ. of Science and Technology of China June 22, 2007 Topics on charmonium hadronic decays Qiang Zhao Theory Division Institute of High Energy Physics, CAS Email: zhaoq@ihep.ac.cn

  2. Outline • Charm quark and charmonium spectrum • “ puzzle” and “12% rule” in J/, ’  V P ( V= , , , K*; P = , , , K) • Isospin violations in V  V P, e.g. , J/   0 • Scalar glueball search in charmonium hadronic decays • Summary

  3. Quarks as building blocks of hadrons: meson (qq), baryon (qqq) • Quarks are not free due to QCD colour force (colour confinement). • Chiral symmetry spontaneous breaking gives masses to quarks. • Hadrons, with rich internal structures, are the smallest objects in Nature that cannot be separated to be further finer free particles. Convention (Particle Data Group): 1) Quark has spin 1/2 and baryon number 1/3; 2) Quark has positive parity and antiquark has negative parity; 3) The flavor of a quark has the same sign as its charge.

  4. 探索物质的微观结构 强子(重子+介子) 是目前能从物质中分离出来、具有内部结构的最小单元。 • 原子 – 10–10 m • 原子核 – 10–14 m 电磁探针  • 核子(质子,中子) – 10–15 m 强子物理 光子 E= 2×197.3 MeV·fm/ • 核子内部(夸克-胶子)自由度 (0.1~0.5)×10–15 m • 产生新强子(, , K…)

  5. Charm quark and charmonium state Parity: P=(1)L+1 Charge conjugate: C=(1)L+S S=0 c c J/ L S=1 c c  L ……….

  6. Charm quark and charmonium states 1976 Nobel Prize: B. Richter and S. C.-C. Ting "for their pioneering work in the discovery of a heavy elementary particle of a new kind" Mass (MeV) n=1 '(3686) c0(3414) n=0 J/(3096) c(2980) 0 (L=0,S=0) 1 (L=0,S=1) 0 (L=1,S=1)

  7. Vector meson production in electron-positron collision e+ * J/ e- Beijing Electron-Positron Collider

  8. J/ hadronic decay DD threshold Mass (MeV) c(2980)  J/(3096) c(2980) Light mesons , , K*K, … 0 (L=0,S=0) 1 (L=0,S=1)

  9. Why study charmonium hadronic decays? • A probe of strong QCD dynamics q Meson c glue q J/ q c Meson q Glue rich intermediate states Lattice QCD 0++: 1.5 ~ 1.7 GeV Exp. Scalars: f0(1370) f0(1500) f0(1710) f0(1790) (?) f0(1810) (?) f0 Lattice QCD prediction Close & Zhao, PRD71, 094022(2005); Zhao, PRD72, 074001 (2005)

  10. A flavour filter for Okubo-Zweig-Iizuka (OZI) disconnected transitions = (uu+dd)/2  = ss V= (I=0) (I=0) c c J/ J/ uudd (I=0) qq (I=1) c c ss(I=0) • Structure of the light hadrons: qq, glueball, multiquark, hybrid … • OZI rule violations • Isospin violations

  11. Focus • Exclusive decays of J/, '  Vector + Pseudoscalar OZI singly or doubly disconnected process “12% rule” for J/ and ‘ and “ puzzle” • Isospin violated process: , J/, '  0 , and its correlation with the OZI-rule violation OZI doubly disconnected process Separate the EM and strong isospin violating processes

  12. “12% rule” and “” puzzle • 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*

  13. Theoretical explanations: • 1. J/   is enhanced • J/-glueball mixing: • Freund and Nambu, Hou and Soni, Brodsky, Lepage and Tuan • Final state interaction: • Li, Bugg and Zou • Intrinsic charmonium component within light vectors: • Brodsky and Karliner, Feldman and Kroll • 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 • 3. Others …

  14. Isospin violation process and its implication Particle Data Group Comparable !? V V g c c * J/ J/ P P c* c*

  15. +/ EM + … 3g  +/ EM + … 3g • “12% rule” will not hold if EM transitions are important. • Otherwise, interferences from the EM decays with the strong decays are unavoidable. V c V * * J/ J/ P P c*

  16. Vector meson dominance model  e+ e+ * * V (, ,  …) =  e- e- EM field in terms of vector meson fields: V* coupling:

  17. Vector meson dominance model VP coupling: V* coupling: Transition amplitude:

  18. I. Determine gVP in V   P  V P

  19. II. Determine e/fV in V  e+ e- e+ * V e-

  20. III. Determine gP in P    P  IV. Form factors Corrections to the V*P vertices: All the relevant data are available !

  21. Isospin violated process

  22. Isospin violated process

  23. For the isospin violated decays, the 12% rule has been violated. One cannot expect the 12% rule to hold in exclusive hadronic decays. For those channels exhibiting large deviations from the empirical 12%, their EM contributions to 'VP are also relatively large.

  24. Evidence for large EM transition interferences in : Large branching ratio differences exist between the charged and neutral K*K-bar implies significant isospin violations. A Right = Left = with

  25. B Right = Left = C Left = Right = D Left = Right =

  26. Including EM and strong transitions (G. Li, Q. Z. and C.H. Chang, hep-ph/0701020)

  27. A brief summary • For the isospin violated decays, the 12% rule has been violated due to the contributions from the form factor corrections. One cannot expect the 12% rule to hold in exclusive hadronic decays. • For those channels exhibiting large deviations from the empirical 12%, their EM contributions to ’  VP are also relatively large. Interferences from the EM transitions are important in the branching ratio fraction between J/psi and psi-prime. This could be one of the sources causing the large deviations from the empirical 12% rule (Zhao, Li and Chang, PLB645, 173 (2007)). • One has to combine the strong interaction in the study of “ puzzle”, and this has been done in a QCD factorization scheme (Li, Zhao and Chang, hep-ph/0701020).

  28. Isospin violations in V  V P • Two sources: • I) Isospin violation via electromagnetic decays • EM interaction does not conserve isospin • II) Isospin violation in strong decays • u and d quark have different masses • Correlation with the OZI rule violation

  29. Isospin violation in    0  (I=0) g s  (I=0) 0 (I=1) s  (I=0) s *  (I=0) 0 (I=1) s

  30. Isospin violation in    0 I) EM process in VMD:

  31. Decompose the EM field in terms of vector mesons in Process-I:

  32. II) Isospin violation in strong decays: • Physical vacuum is not invariant under chiral symmetries • Chiral symmetry is spontaneously broken: Current quarks are no longer massless • Chiral symmetry is explicitly broken: mu md Manifestations: • Light 0 octet mesons (Goldstone bosons), , K,  • Strong isospin violation: m(0) < m(); m(K0) > m(K); m(p) < m(n) …

  33. Strong isospin violation • via intermediate meson exchanges If mu = md, (a)+(b) = 0 and (c)+(d) = 0. If mu md, (a)+(b)  0 and (c)+(d)  0. Li, Zhao and Zou, arXiv:0706.0384[hep-ph]

  34. Three schemes for the intermediate meson exchange loops 1. On-shell approximation 2. Feynman integration with a monopole form factor 3. Feynman integration with a dipole form factor

  35. 1. On-shell approximation 0, No form factor n = 1, monopole 2, dipole  (GeV) : to be determined by experimental data.

  36. Numerical results : Experimental branching ratio: On-shell approximation underestimates the data. Exclusive KK(K*) loop

  37. -dependence of the sum of EM and KK(K*) loop EM and KK(K*) out of phase EM and KK(K*) in phase Still underesitmate the experimental data.

  38. 2. Feynman integration with a monopole form factor  Similarly for the neutral meson loop …

  39. -dependence of the exclusive KK(K*) loop with a monopole form factor

  40. -dependence of the exclusive KK*(K) loop with a monopole form factor

  41. 3. Feynman integration with a dipole form factor Exclusive KK(K*) loop contribution to BR

  42. Exclusive KK*(K) loop contribution to BR

  43. Inclusive contributions from the isospin violating transitions Isospin violation = EM  Strong decay loops V  V P is a P-wave decay, favors a dipole form factor. In phase Out of phase Exp. Exp.

  44. Summary • The correlation between the OZI-rule violation and strong isospin violations makes the intermediate meson exchange process a possible dynamic solution for separating the EM and the strong isospin violation mechanisms. • Application to the study of a0(980)-f0(980) mixing in J/  a0(980)  0 (J.J. Wu, Q.Z. and B.S. Zou, Phys. Rev. D in press). • Experimental focuses of BES, CLEO-c, KLOE, B-factories…

  45. Thanks !

  46. Scalar meson structures probed in charmonium hadronic decays • Conventional and unconventional meson • Scalar mesons between 1~2 GeV • Scalar glueball-qq mixing • Scalar meson production in charmonium hadronic decays

  47. Meson spectroscopy I) QQ mesons Quarks as building blocks of hadrons: meson (qq), baryon (qqq) Convention (Particle Data Group): 1) Quark has spin 1/2 and baryon number 1/3; 2) Quark has positive parity and antiquark has negative parity; 3) The flavor of a quark has the same sign as its charge.

  48. Conventional QQ mesons: • Mesons are bound state of QQ with baryon number B=0; • The parity is given by P=(1)L+1with orbital angular momentum L; • The meson spin J is given by |LS| < J < | L+S| , where S=0, 1 are • the total spin of the quarks. • 4. Charge conjugate is defined as C=(1)L+S for mesons made of quark • and its own antiquark. For light quarks: u, d, and s, the SU(3) flavor symmetry constrains the number of flavor QQ multiplet: 3  3 = 8  1 3 4 1 1

  49. II) Non-QQ mesons Type (a): JPC are not allowed by QQ configuration For states in natural spin-parity series P=(1)L+1 =(1)J , the state must have S=1 and hence CP=(1)(L+S)+(L+1) =+1. Therefore, mesons with natural spin-parity but CP= 1 will be forbidden, e.g. 0+, 1+, 2+, 3+, … L + Natural: 0++, 1, 2++, 3, … Unnatural: ( 0), 1++, 2,3++, …  S=1 L + Unnatural: 0+, 1+, 2+, 3+, …  S=0

  50. Exotic type 1: Mesons have the same JPC as a QQ, but cannot be accommodated into the SU(3) nonet: 3  3 = 8  1 3 4 1 1 f0(1810) f0(1790) Mass f0(1710) Glueball ? QQ-glue mixing ? f0(1500) f0(1370) (1020) (958) f0(980) Jaffe’s Multiquarks? Meson molecule ? (782) /f0(600) (547) 0 1 0 I=0

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