Light scalars as tetraquarks: decays and mixing with quarkonia

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Light scalars as tetraquarks decays and mixing
with quarkonia

• Francesco Giacosa
• Erice
• 17/09/07

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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

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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
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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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Physical input
The light scalars are interpeted as tetraquark
state
A tetraquark is the bound state of two diquarks
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M lt 1 GeV
Tetraquark interpretation
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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)
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Under SU(3)-flavor the 3 diquarks behave like
antiquarks
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Strong decays within a hadronic model flavor
invariance
Nonet of pseduoscalar states
Nonet of scalar tetraquark states
The phys. resonances result from mixing
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Write the , P, C invariant interaction
Lagrangian for the scalar 4q decays
The trace structure corresponds to the
microscopic diagrams
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Decay amplitudes as functions of dominant and
subdominant constants
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(Bugg06)
Non-trivial agreement then all the other ratios
are determined
Ratios stable, not full values
Baru et al, EPJ A23 (2005)
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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
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Typical results for a0 and f0 (MeV)
Full widths can vary, not the ratios. Anyway,
tendentially to relativ. large widths
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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 .

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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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Scalar Quest
M lt 1 GeV 1
GeV lt M lt 2 GeV
These are (mostly) 4q-states!!!
These are (mostly) quarkonia (with
glueball-intrusion)!!!
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A tetraquark condensate is generated
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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
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Thank you
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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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Lattice
GeV
lightest predicted glueball
Morningstar (1999)
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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)
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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
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c c
J/y
G
have been seen
SLAC, e/e-
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have been seen
WA102
have been seen
Crystal Barrel
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Compatible with a dominant
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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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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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The light scalars, interpeted as tetraquars, are
in agreement with basic phenomenology
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Further.finite width.. Beyond
t-lmixingadmixture 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
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• Summary
• Scenario light scalars lt 1 GeV as 4q-states,
  scalars between 1-1.8 GeV as quarkoniaglueball
• Strong 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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