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Study of Diquark-Antidiquark Mesons: A New Spectroscopy?

This work in progress explores the possibility of diquark-antidiquark mesons and their spectroscopy. Recent evidence and studies on sub-GeV scalar mesons suggest a new approach to understanding their properties and decays. The proposed model predicts a rich spectroscopy, including the existence of X(3872) and X(2632) states. Further investigations are ongoing to explore the spin-independent interactions and heavy quark interactions.

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Study of Diquark-Antidiquark Mesons: A New Spectroscopy?

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  1. Mesoni Diquark-antidiquark: una nuova spettroscopia?Work in Progress con F. Piccinini, A. Polosa, V. Riquer Luciano MAIANI, Univ. di Roma1. Italia; INFN, Roma. Italia

  2. Mesoni tetraquark • Un’ idea popolare negli anni ‘70 • QCD incoraggia a pensare che siano possibili • In particolare i mesoni a(980), f(980) ne hanno l’ aspetto • Cruciale l’ esistenza di partner leggeri: s e k • Alternativa: “molecole” K-Kbar, legate da 1-p exchange, come i nuclei • Esp. recenti, a FNAL(E791) e Frascati, hanno “rivisto” il s e riaperto il problema • …e ci sono stati con charm (hidden/open) che non sono/sembrano q-qbar: X(3872), X(3940), (Belle, Babar nei decad. di B+), X(2632) (SELEX)… L.MAIANI. Scalar Mesons & 4-quarks

  3. Sommario • Attrazione e repulsione in QCD • Strutture a “stringa”: il modello del “barionio” (Rossi & Veneziano, 1977) • I mesoni scalari leggeri (hep-ph/0407017, PRL to appear) • Decadimenti in mesone-mesone • Tetraquark con c-cbar: • forze ~ spin indipendenti, molti piu’ stati • Allineamento alle masse dei quark, breaking di isospin • Tetraquark in onda S e X(3872): lo spettro associato. • La particella di SELEX , X(2632), possibile spettro • Conclusioni L.MAIANI. Scalar Mesons & 4-quarks

  4. Ms= f(1020)p0p0g Study of the Decay f(1020)p0p0g with the KLOE Detector The KLOE Collaboration arXiv:hep-ex/0204013 Apr 2002 Sigma parameters from E791 L.MAIANI. Scalar Mesons & 4-quarks

  5. R octet = +1/3 repulsion singlet = -8/3 attraction 1 2 “3bar” = -4/3 attraction “6 “ = +2/3 repulsion Spin-spin interaction R spin 1= +1/2 repulsion spin 0= -3/2 attraction Attractive & repulsive channels in QCD Interaction of two colored objects: • Baryons in the octet: • L=([ud] J=0 s); S0 =({ud}J=1s)L is lighter than S L.MAIANI. Scalar Mesons & 4-quarks

  6. Diquark: [qq] in color = 3bar, spin=0, SU3 flavour = 3bar makes a simple unit to form color singlets (Jaffe..more recently Jaffe&Wilcezck, Karliner & Lipkin for penta-quark) a new topology (Rossi&Veneziano) more related to B-B bar: if you stretch the string, [qq][qbar qbar] B Bbar pair Diquark needs to combine with other colored objects [qq] baryon (e.g. L), Y-shape [qbar qbar]  scalar meson, meson-meson molecules also suggested. But: do “residual” forces bind? L.MAIANI. Scalar Mesons & 4-quarks

  7. t-channel: q qbar mesons s-channel: qqq baryons (no exotics!!) The color junction Duality in Meson-Baryon scattering L.MAIANI. Scalar Mesons & 4-quarks

  8. t-channel: q qbar mesons s-channel: [qq][qbar qbar] (Baryonium) Color junctions What about Baryon-Antibaryon scattering ? [qq][qbar qbar] mesons are dual to q qbar mesons in B-Bbar scattering. The relation to B-Bar persists in decays!! L.MAIANI. Scalar Mesons & 4-quarks

  9. The present work • Recent evidence for s at low energy (E791, then KLOE) led us to reconsider the case of sub-GeV scalar mesons. Many previous investigations (Joffe, Close&Tornqvist, Schecter and coll...). • We propose: • all scalars below 1 GeV are diquark-antidiquark bound states (1 nonet), the q-qbar scalar nonet (L=1, S=1, J=0) has to be above. • Results: • Low energy states show inverted mass spectrum, consistent with “perfect mixing”; • Strong decays are reasonably accounted for; • Decays f S g still to be studied; • Relations with ealier proposal by Rossi&Veneziano suggests connection to Baryon-Antibaryon, rather than Meson-meson states (or molecule) • A rich new spectroscopy is predicted in charm and beauty: X(3872), X(2632)… • Heavy quark intcs: spin independent: new spin states? A work in progress L.MAIANI. Scalar Mesons & 4-quarks

  10. Quantum numbers and mass formula = diquark masses L.MAIANI. Scalar Mesons & 4-quarks

  11. + 4 parameters, 4 masses+1 mixing, one overall relation: • Almost “ideal mixing” • Linear mass formula gives very similar results • With Linear m.f., parameters related to diquark masses: a=480 MeV, b = 250 MeV • Note: a-b=230 MeV vs ms=150 MeV. L.MAIANI. Scalar Mesons & 4-quarks

  12. No derivative coupling! Strong Decays L.MAIANI. Scalar Mesons & 4-quarks

  13. A=2.6 GeV 1. L.MAIANI. Scalar Mesons & 4-quarks

  14. L.MAIANI. Scalar Mesons & 4-quarks

  15. The full SU(3) effective lagrangian... has three couplings: L.MAIANI. Scalar Mesons & 4-quarks

  16. Diquark-antidiquark decays = switch amplitude a = amplitude b Decay proceed via B- Bbar virtual states! Should we try the same for fSg ? L.MAIANI. Scalar Mesons & 4-quarks

  17. M1 M2 Quark rearrang. L.MAIANI. Scalar Mesons & 4-quarks

  18. Maybe f pp comes from “one-loop”: Still too low. (Baryonium picture, see later) or perhaps (!!) c should be small: with c=0 we get G(ahp)=30 MeV vs 6013MeV Overall we get quite a consistent picture, reconciles s with a and f widths, reinforces [qq][qbar qbar] assignement L.MAIANI. Scalar Mesons & 4-quarks

  19. Tetraquark con c-cbar (Work in progress) • L’ interazione spin-spin tra quark pesanti e’ O(1/M) • Se diquark S=0 si legano, anche S=1 • Tutti gli stati (0+1)x(0+1)= 0(x2)+1(x3)+2(x1) • Self-energia: bilancio tra due effetti • Annichilazione: u ubar <-> d dbar, etc.: da’ una matrice con tutti 1 • Autovettori :autostati di SU(N) • Massa dei quark: gli autovettori sono gli stati con tipo definito di quark (es. w/f mixing) • Alla scala del charmonio dovrebbe vincere la massa dei quark (R&V,MPPR) • Gli autovettori sono [cu][cbar ubar], [cd][lcbar dbar],. e non I=1,0 • Belle osserva: X -> J+r, J+ w con simili B.R.!!!! Un nuovo fenomeno L.MAIANI. Scalar Mesons & 4-quarks

  20. Stati: [cu]S=0,1 [cbar ubar]S=0,1 Prediz. input L.MAIANI. Scalar Mesons & 4-quarks

  21. Stati: [cu]S=0,1 [sbar ubar]S=0,1 input DsJ(2457) 1+? Prediz. DsJ(2317) 0+? L.MAIANI. Scalar Mesons & 4-quarks

  22. L.MAIANI. Scalar Mesons & 4-quarks

  23. Interferenza ! L.MAIANI. Scalar Mesons & 4-quarks

  24. Conclusions • A convincing picture of light scalars as [qq][qbar qbar]states: • Masses • Ideal mixing • Decays reasonably described (exact SU3!) but for OZI violating (??) • Annihilation amplitudes are small: • Note: Dm(f-a)~10MeV, Dm(up-down) ~5MeV: are f/a I-spin eigenstates? • New phenomena • States [cq][cbar qbar] and [cq][cbar qbar] should be very visible • I-spin breaking expected maximal in certain decays • SELEX particle: is it the first case? • X(3872) a good candidate, X(3940) predicted Study of F decays in KLOE very important WERE ARE THE EXOTIC STATES??? ! L.MAIANI. Scalar Mesons & 4-quarks

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