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Exploring Gluonic Excitations in the Charmonium Region

This study examines the dynamic and structural aspects of hadrons, focusing on gluonic excitations in the charmonium region. The research delves into topics such as hard probes, flavor symmetries, JPC exotica, and heavy quarkonium characteristics. The collaborators analyze Fock space expansion, exotic channels, and the IR behavior of Yang-Mills Green's function. The study explores resonances above the open charm threshold, string breaking phenomena, and wavefunction distinctions using the Franck-Condon principle. Additionally, the investigation addresses the distribution of momentum and off-planes in meson subsystems for better understanding of hadron structures.

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Exploring Gluonic Excitations in the Charmonium Region

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  1. Gluonic excitations in the Charmonium region Hirschegg’07 Dynamic and structure of hadrons January 16th, 2007 Felipe J. Llanes-Estrada Univ. Complutense Madrid 1

  2. Hadron structure is filtered 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 Heavy quarkonium above threshold, p-distribution of open flavor decays 2

  3. Fock space expansion Collaborators: S. Cotanch, E. Swanson, A. Szczepaniak, I. General, Ping Wang, P. Bicudo 3

  4. qq qqg qqqq gg ggg qq X - - qqg - X - - qqqq - - X gg - X - ggg - X Exotic channel JPC=1- + 4

  5. 5

  6. Trigonometric or hyperbolic Bogoliubov rotation generates a quasiparticle mass gap 6

  7. Model Hamiltonian: Treat physical gluon exchange in perturbation theory Take V as a classical Cornell potential between charge densities 7

  8. Tamm-Dancoff approximation 8

  9. 9

  10. IR Behavior of a connected, fully amputated Yang-Mills Green’s function in Landau gauge with 2n ghost and m gluon legs Alkofer, Fischer, Llanes-Estrada, PLB05 10

  11. Spectrum In quark sector Llanes-Estrada,Szczepaniak,Swanson, Cotanch, PRC04 11

  12. 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 12

  13. y(4260) y(4320) 13

  14. 14 Resonances above open charm threshold

  15. Gamow resonances? DD p-wave r(cc) 15

  16. “String breaking” in lattice computations SESAME Collaboration G. Bali et al prd2005 16

  17. Distinguish the wavefunctions Franck-Condon principle (1925) Molecular transitions between two adiabatic levels: nuclei are not affected by the fast electronic jump. 17

  18. 18

  19. Consider relative momentum distribution of DD subsystem in DDp final state 19

  20. 20

  21. 21

  22. 22 The hybrid p distribution has no shoulders

  23. To test the idea with a sharper signal: Belle run at the Y(5S) Look at the momentum distribution of BB in the BBp final state. Search for a new vector state in Ypp (to have a supernumerary matching the 4260) between the 4S and 5S. (W.S. Hou) 23

  24. s1 s3 L13 s2 s4 L24 L12-34 sd q q  jd q 1 3 q  S sd q q  2 4 jd q J L13+L24 +L12-34 S+L12-34 P = (-1) C = (-1) 24

  25. GROUND STATE S-waves only : 0 P-wave: 1 (0 1 2 3) (0 1 2)  (with various multiplicities) Rich spectrum “state inflation” hopefully most are too broad. 25

  26. Badalyan (1987; Dafne 1991 LNF-91/017 (R)) Jaffe (1977) M (4 light q´s) = 1565 1450 MeV M (2 light 2 s) = 1950 1800 MeV M (4 s q´s) = 2260 2150 MeV JPC = 1states (Mulders, Aerts, de Swart) 1500,1660,1830,1860,1940,2000,2070,2140, 2210... P-wave exotica 1 from 1700 26

  27. Wang, General, Cotanch,FLE upcoming 1)Molecules are lighter (in agreement with Isgur and Weinstein) 2)About every other new state has a match 3)1-+ in the 1.3-1.4GeV ballpark (hybrids well above 2GeV) 27

  28. In the cm frame of a hybrid, momenta and stresses lie instantaneously in a plane 28

  29. However, for a tetraquark there is off-plane stress 29

  30. Consider pure four-body (rare strong) decays (p1xp2).p3 Area of faces Choose any 3 mesons p1+p2+p3+p4=0 (center of mom.) 30

  31. 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 31

  32. For a hybrid For a 4q Internal distribution of off-planes # counts P 32

  33. Maximum: 0.707 P=0.59 (1,2,3) cube 33

  34. To distinguish charmonium from cscs tetraquark 34

  35. Counting rules for inclusive production in e-e+ collider Limit of the cross section as x 1 x= Ey(4260)/Ebeam cc: (1-x) ccg: (1-x)3 J.Gunion PLB79 x 1 35

  36. Counting rules for exclusive double charmonium production Bodwin, Lee and Braaten prl2003 e-e+J/y y(4260) r = 2mc/Ebeam Fixed angle production when r 0 ds/dxconstant for cc r2 for ccg 36

  37. 0++ L=0 1++ 2++ 0  L=1 2  3  YLm <s1 m1 s2 m2 | S mS> Coulomb gauge BCS-TDA glueballs (A. Szczepaniak et al. PRL 76, 2011 (1996), F. Llanes-Estrada et al. NPA (2002).) 37

  38. GLUEBALLS (Lattice spectrum from Morningstar and Peardon) 38

  39. Glueballs fall on Regge Trajectories * Interaction between color densities as suggested by QCD in the Coulomb gauge (non abelian gluon-gluon interaction) * Slope of Regge trajectories much smaller than for quark mesons because color factor 3 instead of 4/3 * In (L,S) notation: model (0,0) 0, (2,0) 2, (4,0) 4++ fall on Regge trajectory parallel to pomeron. * The 2 (0,2) falls on Pomeron Regge trajectory, within lattice error bands. * These are little sensitive to spin-orbit coupling which is the model’s largest weakness. 39

  40. F.J.L.E. et al. 2000 40

  41. Three body sector: hybrids, oddballs 41

  42. Oddball Regge trajectories 42

  43. Glueball decay width Previous estimates: O(10-30) MeV Carlson et al OZI O(150) MeV Bicudo, Abreu string O(400) MeV Cotanch, Williams VMD Our new evaluation: Bicudo, Cotanch, Ll-E, Robertson 2006 43

  44. 47 Motivation: new BES state f0(1810) (600,1370,1500,1710,1790) J/ Angular analysis shows quant. numbers 0++ Threshold cusp? No. Tail of the f0(1710)? Adjust for phase space and still off-threshold 44

  45. Should have been visible in at DM2 48

  46. But DM2 could not have seen it in  49

  47. Prefered decay modes: open flavor • For C=+ charmonia this is an experimental fact • For glueballs it is expected on the basis of string breaking • For radiative J/y decays... as much as a glueball in the middle 50

  48. 51

  49. 52

  50. 53 In the end, glueballs are not so broad... Many dynamical effects dispell the legend of the flavor-blind glueball decays

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