Light scalars as tetraquark states

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Light scalars as tetraquark states

• Francesco Giacosa
• Hirschegg
• 18/01/07

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Francesco Giacosa
Scalar Quest

• Outline
• Problems of the light scalar mesons
• Interpretation of the light scalar mesons
  interpreted as tetraquark-states (Strong and e.m.
  decays, hadronic d.o.f)
• Mixing of tetraquark and quarkonia
  configurations
• Outlook and Summary

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Francesco Giacosa
Scalar Quest
Scalar Mesons below 1.8 GeV listed in PDG
M lt 1 GeV 1
GeV lt M lt 1.8 GeV
Too many resonances than expected from
quark-antiquark states
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Francesco Giacosa
Scalar Quest
Francesco Giacosa
Scalar Quest
M lt 1 GeV
interpretation
Assignement has problems!!!
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List of Problems
Francesco Giacosa
Scalar Quest

• 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
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Francesco Giacosa
Scalar Quest
Tetraquark interpretation

• Jaffes 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
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Francesco Giacosa
Scalar Quest
Under SU(3)-flavor the 3 diquarks behave like
antiquarks
Example
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Francesco Giacosa
Scalar Quest
M lt 1 GeV
Tetraquark interpretation
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Francesco Giacosa
Scalar Quest
Previous works and motivations
Strong decays of a tetraquark state
Jaffe-orig Jaffe, Phys. Rev. D 15 (1977),
Bugg-06 hep-ex/0603089 Maiani Maiani et al,
Phys. Rev. Lett. (2004)
Systematic evaluation of amplitudes My work
Giacosa, Phys. Rev. D 74 (2006)
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Francesco Giacosa
Scalar Quest
Strong decays within a hadronic model (never see
quarks and gluons, only hadrons)
Nonet of pseduoscalar states
Nonet of scalar tetraquark states
The phys. resonances result from mixing
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Francesco Giacosa
Scalar Quest
Write the flavor, P, C invariant interaction
Lagrangian for the scalar 4q decays
The trace structure corresponds to the
microscopic diagrams
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Francesco Giacosa
Scalar Quest
Decay amplitudes as functions of dominant and
subdominant constants
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Francesco Giacosa
Scalar Quest
(Bugg06)
Non-trivial agreement then all the other ratios
are determined
Imp without the subdmominant one has
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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.
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Francesco Giacosa
Scalar Quest
M lt 1 GeV 1
GeV lt M lt 2 GeV
These are 4q-states!!!
These are quarkonia (with glueball-intrusion)!!!
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Francesco Giacosa
Scalar Quest
Extension tetraquark-quarkonia mixing (sketch)

• 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, hep-ph/0611388)

P, S
P, S
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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 !!!
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Francesco Giacosa
Scalar quest

• Summary
• Scenario light scalars lt 1 GeV as 4q-states,
  scalars between 1-1.8 GeV as quarkoniaglueball
• Strong and e.m. decays (outlook about vector
  mesons)
• My last result mixing of 4q and quarkonium
  occurs but it is small.
• Understanding of the scalar sector lt 2 GeV is
  important to study the decay of states in the
  charmonia region.

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Francesco Giacosa
Scalar Quest
Thank you very much!!!