Fock space expansion The shell-model of hadron physics

1. Fock space expansion The shell-model of hadron physics Collaborators: S. Cotanch, E. Swanson, A. Szczepaniak, I. General, Ping Wang, P. Bicudo -6

2. Fock Space Expansion: | qq > + | qqqq > + | gg > + | qqg > + | qqqqqq > . . . Whatever is not forbidden is mandatory: “This state is an (X) state” misleading when strong mixing. -5

3. Convergence: trigonometric or hyperbolic Bogoliubov rotation generates a quasiparticle mass gap. -4

4. Large Nc limit Collaborators: J. R. Pelaez and Guillermo Rios -3

5. qq qqg qqqq gg ggg qq X - - qqg - X - - qqqq - - X gg - X - ggg - X Exotic channel JPC=1- + -2

6. Hadron structure is filtered -1 q, g (as, mq) Confinement p, r, h ... (Mh, fh, li ...) Can peep through with 1) Hard probes 2) Flavor symmetries 3) JPC exotica 4) Detailed branchings 5) Counting rules in production Momentum distribution of decay products

7. The Franck-Condon principle and exotic hadrons SCADRON70 SCAlar haDRON February 17th, 2008 Felipe J. Llanes-Estrada Univ. Complutense Madrid 0

8. Outline • The Franck-Condon principle • The Sturm-Liouville nodes and quarkonium (conventional vs. hybrid) • Tetraquarks and off-planes correlator • Testing meson decay mechanisms 1

9. Edward U. Condon James Franck Some old timers... 2

10. Distinguish the wavefunctions Franck-Condon principle (1925) Molecular transitions between two adiabatic levels: nuclei are not affected by the fast electronic jump. 3

11. It neatly explains the phenomenon of fluorescence in molecular physics (See book by Herzbach or even Wikipedia) 4

12. What about it in hadron physics? Heavy quarks: nuclei Gluons, pions... : electrons Conjecture (obvious in the heavy quark limit) When a hadron decays, the relative momentum distributions of the hadron products containing a heavy quark, coincide with the initial momentum distributions ot those quarks in the parent hadron. 5

13. Outline • The Franck-Condon principle • The Sturm-Liouville nodes and quarkonium (conventional vs. hybrid) • Tetraquarks and off-planes correlator • Testing meson decay mechanisms General, Cotanch, Llanes-Estrada, EPJC51:347-358,2007 6

14. y(4660) y(4320) y(4260) Llanes-Estrada, Cotanch PLB504:15-20, 2001 7

15. Glueish mesons in the 4-5 GeV region 1) High-pitch glueballs 2) Oddballs 3) Hybrid mesons Confused with: some conventional cc And a multitude of 4+q states 8

16. 9 FJLE PRD72 031503 2006 Resonances above open charm threshold

17. 10 (Measured in the nuclear shell model)

18. Consider relative momentum distribution of DD subsystem in DDp final state 11

19. 12

20. 13

21. 14 The hybrid p distribution has no shoulders

22. To test the principle with a sharper signal: Belle run at the Y(5S) Look at the relative momentum distribution of BB in the BBp final state. b b p BB 15

23. Outline • The Franck-Condon principle • The Sturm-Liouville nodes and quarkonium (conventional vs. hybrid) • Tetraquarks and off-planes correlator • Testing meson decay mechanisms General et al, PLB653:216-223,2007 16

24. In the cm frame of a hybrid, momenta and stresses lie instantaneously in a plane 17

25. However, for a tetraquark there is off-plane stress 18

26. Consider pure four-body (rare strong) decays (p1xp2).p3 Area of faces Choose any 3 mesons p1+p2+p3+p4=0 (center of mom.) 19

27. Observable: off-planes: ((p1xp2).p3)2 P= (|p1xp2| |p2xp3| |p1xp3| |p1xp4| |p2xp4| |p3xp4|)1/2 1)Dimensionless 2)Permutation invariant (1,2,3,4) in the cm frame 3)Vanishes for 2,3-body intrinsic wavefunctions 20

28. ? For a hybrid For a 4q Internal distribution of off-planes # counts P 21

29. Maximum: 0.707 P=0.59 (1,2,3) cube 22

30. 23 RGM (Ribeiro, Bicudo) attractive Example: Belle’s record pion Z(4430) y’ p ud + udg + ccud + ... Has been suggested to be a D1 D* molecule For the Coulomb-gauge model with meson- meson type clusters, can compute correlator

31. Z p pDD 24

32. Outline • The Franck-Condon principle • The Sturm-Liouville nodes and quarkonium (conventional vs. hybrid) • Tetraquarks and off-planes correlator • Testing meson decay mechanisms 25

33. Relative wavefunction of the pair? Old question of the quark model 26

34. 27 However quark model claims are that 3P0 fits best So a quark-antiquark should naturally be emitted as a 3S1 pair A gluon has JP 1-

35. But we don’t know yet the Ds-Ds Hermes: sea quarks are unpolarized 28

36. b-quark c-quark DKK (B below DDD threshold) B-meson undergoes semileptonic decay (about 10% branch) DD (About 1% of above) u-quark Test mechanism with Franck-Condon 29

37. Application of the Franck-Condon principle: the momentum distribution of DD gives the distribution of cc created inside B meson (and other hadrons) B lnl+DKK+Xud(Large branching fraction theoretically less clean) B lnl+DD+Xud (10-5 but more reliable) 30

38. Conclusions • The Franck-Condon principle could provide the intelectual framework to decide on intrinsic wf based on decay output in model independent way • Testable on Y(5S) to BBp • y(4260) to DDp hybrid or charmonium? • Z(4430) and others, how much 4-quark? • Semileptonic or not, semiinclusive B to DD, direct test of 3P0 pair creation mechanism 31

39. The Franck-Condon principle and exotic hadrons SCADRON70 SCAlar haDRON February 17th, 2008 Felipe J. Llanes-Estrada Univ. Complutense Madrid 32