1. 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 2/182010 Dec. 7~11 BARYONS’10

3. Motivation : Di-quark Structures in Hadrons SHLee and S.Yasui : EPJ C (2009) 3/18 2010 Dec. 7~11 BARYONS’10

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

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

6. Introduction: QCD Sum Rules ∼ Spectral Density Ex) 6/18 2010 Dec. 7~11 BARYONS’10

7. Introduction: QCD Sum Rules 7/18 By the weight function, high resonances are suppressed. 2010 Dec. 7~11 BARYONS’10

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

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

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

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

12. Λ Baryons 12/18 Diquark Mass (GeV)Ratio(λ) 0.2-0.5 0.3-0.2 0.4-0.013 0.410 Parameter Set ( m s =0.12GeV, m Λ =1.115GeV) Parameter Set ( m s =0.12GeV, m Λ =1.115GeV) 2010 Dec. 7~11 BARYONS’10

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

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

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

16. Scalar meson 16/182010 Dec. 7~11 BARYONS’10

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. 17/182010 Dec. 7~11 BARYONS’10

18. Thank you!