Multiquark States from a QCD sum rule approach with diquark effective fields

Kyungil Kim, Daisuke Jido, Su Houng Lee

June 22nd , 2012, Tokyo, `Heavy Quark Hadrons at J-PARC 2012’

Based on K. Kim, D. Jido, S.H.Lee PRC 84(2011)025204 K. Kim, D. Jido, S.H.Lee in preparation.

Motivation : Di-quark Structures in HadronsSHLee and S.Yasui : EPJ C (2009)

<Diquark inside baryons>

<Quark-antiquark inside mesons>

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Diquark Structures and Heavy-quark

<Tetraquark> qq

h h

<H Dibaryon>

<Pentaquark>

ud

h us

ud

su

ds

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N*, Θcs, …

<Baryon>q

hq Λ, Ξ, …

Λ Baryons

u d

h

<Current for Λ >

Scalar diquark fieldGauge invariant Lagrangian for diquark field

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<Color-spin interaction>

Effective Diquark FieldsGauge invariant Lagrangian for diquark field

The relation between diquark condensate and gluon condensate

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<Propagator of diquark field>

June 22nd 2012

QCDSR with Di-quark fieldsOPE Result

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Λ BaryonsDiquark Mass (GeV) Ratio(λ)

0.2 -0.50.3 -0.20.4 -0.013

0.41 0

Parameter Set ( ms=0.12GeV, mΛ =1.115GeV)

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Λ Baryons

<Lambda_c sum rule> <Lambda_b sum rule>

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Ξ Baryons

<Ξ_c sum rule> <Ξ_b sum rule>

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H-dibaryon

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<Theoretical Prediction of H-dibaryon> <Lattice QCD results>

<HAL collaboration>

<H-dibaryon search in STAR at RHIC>

June 22nd 2012

H-dibaryon

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ud

su

ds

u ds

ud s

<Current choice for H-dibaryon>

<Dispersion relation>∼ Spectral Density

June 22nd 2012

OPE Result (up to Dim. 4)

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Results in SU(3)(flavor) Sym.

<Borel Curves with various threshold>

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Summary & Outlook

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The QCD sum rule approach with diquark fields gives a good result for Λs, Ξs and H-dibaryon.

We can have a diquark mass and condensate values from Lambda.

These parameters give good masses for Lmabda_c and Lambda_b.

In same approach, we can obtain the properties of ‘qs’-di-quark from Ξ_c.

We obtain the mass of H-dibaryon from a QCD sum rule ap-proach with effective diquark fields.

Pentaquarks(N*,Θcs) and tetraquarks(T_cc, T_cb) are also good candidates to apply this approach. (in progress)

June 22nd 2012

Thank you very much!!