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Light scalars as tetraquarks: decays and mixing with quarkonia

Light scalars as tetraquarks: decays and mixing with quarkonia. Francesco Giacosa Erice 17/09/07. Francesco Giacosa Scalar Quest. Outline Brief review of problems of the light scalar mesons Light scalars as tetraquark - states:

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Light scalars as tetraquarks: decays and mixing with quarkonia

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  1. Light scalars as tetraquarks: decays and mixing with quarkonia Francesco Giacosa Erice 17/09/07

  2. Francesco Giacosa Scalar Quest • Outline • Brief review of problems of the light scalar mesons • Light scalars as tetraquark-states: • Mixing of tetraquark and quarkonia configurations: • Outlook and Summary

  3. Francesco Giacosa Scalar Quest Scalar Mesons below 1.8 GeV listed in PDG M < 1 GeV 1 GeV < M < 1.8 GeV Too many resonances than expected from quark-antiquark states

  4. Francesco Giacosa Scalar Quest Francesco Giacosa Scalar Quest M < 1 GeV interpretation Assignement has problems!!!

  5. Francesco Giacosa Scalar Quest List of Problems • Masses: degeneracy of and • Strong coupling of to • The scalar quarkonia are p-wave states (L = S = 1), thus expected to be heavier than 1 GeV as tensor and axial-vector mesons • Some Lattice results find • Large behavior of light scalar not compatible with quarkonia from: Prelovsek et al., Phys. Rev. D 70 (2004), Burch et al., Phys. Rev. D 73 (2006) from: Pelaez, Phys. Rev. Lett. (2004), Pelaez and Rios, hep-ph/0610397

  6. An example of „good diquark” is: (and not ) Example: Francesco Giacosa Scalar Quest Physical input: The light scalars are interpeted as tetraquark state A tetraquark is the bound state of two diquarks

  7. Francesco Giacosa Scalar Quest M < 1 GeV Tetraquark interpretation

  8. P P Dominant [4q] [4q] S S P P Subdominant Francesco Giacosa Scalar Quest Previous works and motivations Strong decays of a tetraquark state: Jaffe-orig: Jaffe, Phys. Rev. D 15 (1977), Maiani: Maiani et al, Phys. Rev. Lett. (2004) Bugg-06: D. V. Bugg, EPJC47 (2006) Systematic evaluation of amplitudes: My work: Giacosa, Phys. Rev. D 74 (2006)

  9. Francesco Giacosa Scalar Quest Under SU(3)-flavor the 3 diquarks behave like antiquarks:

  10. Francesco Giacosa Scalar Quest Strong decays within a hadronic model: flavor invariance Nonet of pseduoscalar states: Nonet of scalar tetraquark states: The phys. resonances result from mixing

  11. [4q] [4q] S S P P P P Dominant Subdominant Francesco Giacosa Scalar Quest Write the , P, C invariant interaction Lagrangian for the scalar 4q decays: The trace structure corresponds to the microscopic diagrams:

  12. S Francesco Giacosa Scalar Quest Decay amplitudes as functions of dominant and subdominant constants

  13. Fit of 2 theor. quantities to 3 exp-known ratios: Francesco Giacosa Scalar Quest (Bugg06) Non-trivial agreement; then all the other ratios are determined: Ratios stable, not full values: Baru et al, EPJ A23 (2005)

  14. Francesco Giacosa Scalar Quest Loops inclusion (sketch): Interpretation: tetraquark seed surrounded by mesonic clouds This is crucial for the full evaluation of the KK decay modes of a0(980) and f0(980) Im[ ] Details in F.G., G. Pagliara, 0707.3594 []hep-ph]

  15. Francesco Giacosa Scalar Quest Typical results for a0 and f0 (MeV): Full widths can vary, not the ratios. Anyway, tendentially to relativ. large widths

  16. Francesco Giacosa Scalar Quest Extension: from flavor to chiral invariance • Scalar tetraquark and quarkonia states can mix (Black et al, Phys. Rev. D 64 (2001), Fariborz et al. Phys. Rev. D 72 (2005) ) • Extension of the model: ; consider scalar and pseudoscalar quarkonia meson and scalar tetraquark states (Giacosa, Phys. Rev. D ... (2007) ) Spontaneous symmetry breaking is assumed, but no need to specify the potential. • Introduce the pseudoscalar diquark: it is a necessary intermediate step to achieve chiral invariance. Couple diquarks to .

  17. [4q] [4q] S S Subdominant Dominant Francesco Giacosa Scalar Quest

  18. Francesco Giacosa Scalar Quest Mixing in the isovector sector In particular: One relates the tetraquark-decay parameters to the mixing strenght; then, one can evaluate the mixing: The mixing is small !!!

  19. Francesco Giacosa Scalar Quest M < 1 GeV 1 GeV < M < 2 GeV These are (mostly) 4q-states!!! These are (mostly) quarkonia (with glueball-intrusion)!!!

  20. Francesco Giacosa Scalar Quest A tetraquark condensate is generated:

  21. Outlook: Francesco Giacosa Scalar Quest Summary and outllok The tetraquark interpretation for the light scalars is in agreement with (some) basic phenomenological properties When including mesonic loops the tetraquark seed gets surrounded by meson-antimeson pairs The mixing with the (heavier) quarkonia is present but turns out to be small

  22. Francesco Giacosa Scalar Quest Thank you

  23. Francesco Giacosa Scalar Quest For the two-photon decays proceed in a similar way: Outlook: decay of (and into) vector mesons. Through VMD no new parameters.

  24. Francesco Giacosa Scalar Quest

  25. Francesco Giacosa Scalar Quest Lattice: GeV lightest predicted glueball Morningstar (1999)

  26. Francesco Giacosa Scalar Quest

  27. Francesco Giacosa Scalar Quest Result for the mixed states: (Fit to two-pseudoscalar decays) has the largest gluonic amount!!! from: F. Giacosa et al., Phys. Rev. D 72 (2005)

  28. Francesco Giacosa Scalar Quest

  29. Francesco Giacosa Scalar Quest The results point to: has a larg gluonic amount in its wave function. We expect to see this state in gluon-rich processes Qualitative argument from experiment

  30. Francesco Giacosa Scalar Quest c c J/y G have been seen SLAC, e+/e-

  31. Francesco Giacosa Scalar Quest have been seen WA102 have been seen Crystal Barrel

  32. Francesco Giacosa Scsalar Quest Compatible with a dominant:

  33. Francesco Giacosa Scalar Quest M < 1 GeV 1 GeV < M < 2 GeV These are 4q-states!!! These are quarkonia (with glueball-intrusion)!!!

  34. Francesco Giacosa Scalar Quest Tetraquark interpretation • Jaffe’s four-quark states can explain the scalar states below 1 GeV: • Out of a diquark and an anti-diquark one can build a nonet of four-quark states with suitable characteristics • A spinless diquark in the flavor and color antisymmetric combination (good diquark) forms a compact object • (1-gluon exchange, instantons, NJL, DSE) Example of a „good diquark”:

  35. Francesco Giacosa Scalar Quest The light scalars, interpeted as tetraquars, are in agreement with basic phenomenology

  36. Francesco Giacosa Scalar Quest Further….finite width….. Beyond t-l…mixing…admixture of meson-antimeson pair…. mass distribution….problem of kaon….ordering….. Here better presentation of the result Discuss briefly the loops Width ordering The seed is the tetraquark, which is then dressed by hadronic clouds

  37. Francesco Giacosa Scalar quest • Summary • Scenario: light scalars < 1 GeV as 4q-states, scalars between 1-1.8 GeV as quarkonia+glueball • Strong decays (outlook about vector mesons) • My last result: mixing of 4q and quarkonium occurs but it is small. • Understanding of the scalar sector < 2 GeV is important to study the decay of states in the charmonia region.

  38. Francesco Giacosa Scalar Quest

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