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A QCD Sum Rule with An Explicit Di-quark Field

A QCD Sum Rule with An Explicit Di-quark Field . Kyung- il Kim, Su Houng Lee, Daisuke Jido. December 7~11, 2010, BARYONS’10 . Contents. Motivation Di-quark Structures in Hadrons Introduction to QCD Sum Rule(QCDSR) QCDSR with Di-quark Eff. Lagrangian Lambda particles Nucleons

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A QCD Sum Rule with An Explicit Di-quark Field

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  1. A QCD Sum Rule with An Explicit Di-quark Field Kyung-il Kim, Su Houng Lee, Daisuke Jido December 7~11, 2010, BARYONS’10

  2. Contents • Motivation • Di-quark Structures in Hadrons • Introduction to QCD Sum Rule(QCDSR) • QCDSR with Di-quark Eff. Lagrangian • Lambda particles • Nucleons • Scalar meson • The Summary 2010 Dec. 7~11 BARYONS’10 2/18

  3. Motivation : Di-quark Structures in Hadrons SHLee and S.Yasui : EPJ C (2009) <Diquark inside baryons> <Quark-antiquark inside mesons> 2010 Dec. 7~11 BARYONS’10 3/18

  4. Motivation : Di-quark Structures in Hadrons <Tetraquark> q u q Vs. u q d d q <Pentaquark> q q q q q <H Dibaryon> q q q q q q 2010 Dec. 7~11 BARYONS’10 4/18

  5. Introduction: QCD Sum Rules <Two-point correlation function> <The operator product expansion> OPE factorizes function into a short- and long-distance piece Example) for gluon operator 2010 Dec. 7~11 BARYONS’10 5/18

  6. Introduction: QCD Sum Rules <Dispersion relation> ∼ Spectral Density Ex) <Optical Theorem> 2010 Dec. 7~11 BARYONS’10 6/18

  7. Introduction: QCD Sum Rules <Borel Transformation> By the weight function, high resonances are suppressed. <Sum rule to obtain mass> 2010 Dec. 7~11 BARYONS’10 7/18

  8. Λ Baryons d u s Ref. PDG <Current for Λ mesons> Scalar diquark field Gauge invariant Lagrangian for diquarkfield 2010 Dec. 7~11 BARYONS’10 8/18

  9. QCDSR with Di-quark fields Effective Lagrangian for Di-quark Field <Propagator of diquark field> =0 =0 2010 Dec. 7~11 BARYONS’10 9/18

  10. Λ Baryons Gauge invariant Lagrangian for diquarkfield Propagator of diquark field Free parameters! The relation between diquark condensate and gluon condensate OPE terms 2010 Dec. 7~11 BARYONS’10 10/18

  11. QCDSR with Di-quark fields OPE Result 2010 Dec. 7~11 BARYONS’10 11/18

  12. Λ Baryons Parameter Set ( ms=0.12GeV, mΛ =1.115GeV) 2010 Dec. 7~11 BARYONS’10 12/18

  13. Λ Baryons mc=1.6 GeV, mΛ =2.284GeV 2010 Dec. 7~11 BARYONS’10 13/18

  14. Nucleons Neutron u d d Proton d u u The masses of nucleons are over 1GeV -> We didn’t consider the tunneling behavior of quarks! 2010 Dec. 7~11 BARYONS’10 14/18

  15. Scalar meson Scalar meson as a tetraquark q q q q (ud-diquark field) Can it reproduce sigma(600) meson? Jaffe(1977) PRD 2010 Dec. 7~11 BARYONS’10 15/18

  16. Scalar meson 2010 Dec. 7~11 BARYONS’10 16/18

  17. Summary • In some hadron configuration, during diquark structures are not broken, we can regard diquark field as a point particle. • Two free parameter, diquark mass and condensate can be chosen from Λ sum rules. These parameters give reasonable mass of Λ_c. • QCD sum rule with diquark field gives nucleon mass as over 1GeV. -> We need to consider tunneling effect of quarks. • We can not reproduce a sigma(600) meson mass because that has not good diquark structure. -> The scalar meson which has a diquark structure has a mass over 1 GeV. 2010 Dec. 7~11 BARYONS’10 17/18

  18. Thank you!

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