A QCD Sum Rule with An Explicit Di-quark Field

1. A QCD Sum Rule with An Explicit Di-quark Field Kyungil Kim, Su Houng Lee, Daisuke Jido August 22th, 2011, in APFB2011 Based on K. Kim, D. Jido, S.H.Lee [arxiv 1103.0826] (accepted in PRC on Aug.)

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 2011 August 22 in APFB2011 2/19

3. Motivation : Di-quark Structures in Hadrons SHLee and S.Yasui : EPJ C (2009) <Diquark inside baryons> <Quark-antiquark inside mesons> 2011 August 22 in APFB2011 3/19

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> Di-quark structure has a important rolein high density phase. q q q q q q 2011 August 22 in APFB2011 4/19

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 2011 August 22 in APFB2011 5/19

6. Introduction: QCD Sum Rules <Dispersion relation> ∼ Spectral Density Ex) <Optical Theorem> 2011 August 22 in APFB2011 6/19

7. Introduction: QCD Sum Rules <Borel Transformation> By the weight function, high resonances are suppressed. <Sum rule to obtain mass> 2011 August 22 in APFB2011 7/19

8. Λ Baryons d u s Ref. PDG <Current for Λ > Scalar diquark field Gauge invariant Lagrangian for diquarkfield 2011 August 22 in APFB2011 8/19

9. QCDSR with Di-quark fields Effective Lagrangian for Di-quark Field <Propagator of diquark field> =0 =0 2011 August 22 in APFB2011 9/19

10. Λ Baryons Gauge invariant Lagrangian for diquarkfield Propagator of diquark field Free parameters! The relation between diquark condensate and gluon condensate OPE terms 2011 August 22 in APFB2011 10/19

11. QCDSR with Di-quark fields OPE Result 2011 August 22 in APFB2011 11/19

12. Λ Baryons Parameter Set ( ms=0.12GeV, mΛ =1.115GeV) 2011 August 22 in APFB2011 12/19

13. Λ Baryons <Variation of threshold (s0)> <Dependence of high order operator> 2011 August 22 in APFB2011 13/19

14. Λ Baryons <Lambda_b sum rule> <Lambda_c sum rule> 2011 August 22 in APFB2011 14/19

15. 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! 2011 August 22 in APFB2011 15/19

16. Scalar meson Scalar meson as a tetraquark q q q q (ud-diquark field) Can it reproduce sigma(600) meson? Jaffe(1977) PRD 2011 August 22 in APFB2011 16/19

17. Scalar meson 2011 August 22 in APFB2011 17/19

18. 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_cand Λ_b. • The QCD sum rule with an explicit diquark field give us reasonable masses for various particles. • -> As a future work, we want to test this sum rule technique • to multi-quark particles (H dibaryon, Pentaquark, …). 2011 August 22 in APFB2011 18/19

19. Thank you!