1. Nov. 12, HAPHY. A QCD sum rule analysis of the PLB 594 (2004) 87, PLB 610 (2005) 50, and hep-ph/0506250 Hee-Jung Lee Vicente Vento (APCTP & U. Valencia) Nikolai Kochelev (JINR & SNU)

2. Contents Introduction Interactions induced by Instantons Diquark-Triquark model for Pentaquark within Instanton model for the QCD vac. QCD sum rule : Triquark correlations and Discussion

3. QCD : The fundamental theory for the strong interaction - Degrees of freedom : quark and gluon Hadrons = Baryons+Mesons Baryons = 3 quarks Mesons = quark+antiquark Multiquark hadrons are possible? YES!? (S=+1 Exotic, etc) Role of Instanton in Multiquark systems? Quark Model

4. T. Nakano et al : PRL 91(2003) 012002 Observed Pentaquark in  n →K + K - n Mass=1540MeV, Width < 25MeV

5. M nK + LEPS

6. (LEPS) F. Close and Q. Zhao, hep-ph/0404075

7. Status of... 1997 : Prediction by Diakonov et al in the chiral soliton model, mass about 1530MeV and width < 15MeV. 2003 : Observation by LEPS. Following it, many (+) results were reported : Jefferson Lab, Russia, SAPHIR… (from reanalyzing data obtained in 1997-98) 2004-2005 : theoretical criticism and (-) results have been emerged.

8. - Null results : most from experiments with higher energy and large statistics using nuclei, hadrons rather than photons  Production depends on production mechanism strongly(?) -Jeffeson Lab this year : hep-ex/0510061 : Upper limit for production cross section of < 0.2% (c.f. 40% in LEPS) Summary : hep-ph/0510309 by Burkert F. Close, Nature,Vol435,19 May 2005

9. from soliton model At the top of Antidecouplet : Mass : 1540 MeV Width < 30MeV Parity = +1(?)

10. Simple constituent quark model based on independently moving quarks yields mass of pentaquark around 2 GeV Correlations of quarks inside of (?) Quark model

11. Two models for pentaquark 1. Jaffe and Wilczek, PRL91(2003)232003 Potential by one gluon exchange Two scalar diquarks (L=1) + a strange antiquark Parity = +1 Recent calculation gives higher mass than observed. (PRL94 (2005) 062001)

12. 2. Karliner and Lipkin, PLB575 (2003) 249 Triquark + diquark + orbital motion (L=1) Interaction by one gluon exchange Triquark = diquark =

13. Mass=1385 (quark masses + OGE) + 207 (orbital motion L=1) = 1592 MeV Parity = +1 Small width : Potential barrier by the orbital motion ?? : - Is there another important source for quark correlations in hadrons? instanton? - Only one state in 3q cluster in KL’s?

14. Instanton : Strong fluctuation of gluonic field in QCD vacuum

15. Interactions induced by Instanton Two body + Three body interactions

16. Some Properties Acts on only quarks with different flavors : flavor antisymmetric wave functions (Isospin=0) Minimal spin Maximal strength Three body interaction by Instanton in colorless 3-quarks state vanishes For interactions with anti-quark:

17. Our Model Interaction by one gluon exchange + Interaction by Instanton Instanton supplies the much smaller strong interaction coupling (~0.5) For pentaquark : with different flavors Diquark + Triquark : separated enough

18. Mass Formula for Hadrons Confinement Masses, m u =m d =m 0

19. Diquark + Triquark System Diquark is in isospin = 0, spin = 0 : due to instanton (ud) quarks in Triquark is in isospin = 0 : due to instanton Triquark is in spin = 1/2 There are two possibilities in Triquark Relative orbital motion : L=1

20. State of each cluster Diquark : Flavor space : Color space : Spin space :

21. Triquark : - A state Flavor space : Color space : Spin space :

22. - B state Flavor space : Color space : Spin space :

23. After diagonalization Masses of clusters from parameters

24. Mass of Pentaquark : - With the energy from orbital motion Orbital motion gives Small width Positive Parity

25. Short summary I Instanton Induced Interaction plays a important role in pentaquark. By the way, are there really two clusters of quarks in pentaquark? Triquark correlations in a QCD sum rule Diquark correlation by Schaefer et al NPB 412(1994) 143

26. QCD sum rules The Correlator of the interpolating current with the quantum number of particle (state) under consideration Calculating it in deeply Euclidean region by the perturbative OPE Condensates from the nonperturbative vacuum Nonperturbative Vacuum

27. is related to physical region by the dispersion relation with a narrow resonance approx. for spin ½ particle case

28. With the Borel transformation, the higher state contributions is exponentially suppressed. Two QCD sum rules : Quark-Hadron duality :

29. Mass of Particle can be determined in the three ways In general, if we include all contribution from OPE, the above ways must give same mass independent on. Actually, we cannot do it. Up to a certain energy dimension operator, in some region of

30. Parity of particle : -With the state of opposite parity to the current is -The interpolating current can create a state of opposite parity to the intrinsic parity of the current :

31. Left hand side on the 2 nd sum rule is + : the same parity as the current Left hand side on the 2 nd sum rule is - : opposite parity to the current

32. The 2 nd sum rule with massless u,d : OPE up to d=5 for nucleon & triquarks :

33. Quark Propagator : By the Wick’s theorem : perturbative vacuum Perturbative propagator color spin Nonperturbative effect : vacuum condensates flavor

35. Nucleon and triquark states Interpolating current for nucleon of positive parity : Energy dimension of correlator for nucleon and color triquark states after the Borel transform : 7 T-product of currents :

36. QCD sum rule without direct instantons: =+=+

37. Instanton effect : zero mode of quark

38. Mass and Residue : With threshold 1.75 GeV and f=1, t=-1

39. A state in Triquark Interpolating currents of (-) parity : QCD sum rule without direct instantons:

40. Interpolating current of (–) parity : QCD sum rule without direct instantons B state in Triquark

41. Instanton effect Two body effects : Three body effect : no in B

42. Masses and residues For A state : threshold 1.8 GeV, f~-t

43. For B state : threshold 1.72 GeV

44. Short summary II Schaefer et al showed (ud)-diquark correlation with mass around 420MeV. Are there really three quark correlations in pentaquark? Two quasi-bound color quark correlations are there. These estimation gives the similar value of mass to in our MODEL. With a current of 5 quarks ?

45. QCD sum rule in 5-quarks Two color clusters in the model : - Diquark and Triquark clusters Diquark cluster : Spin(S)=0, Isospin(I)=0, Color(C)= Triquark cluster : S=1/2, I=0, C=3 Two states in triquark cluster (ud) diquark : in A, S=1/2, I=0, C= in B, S=1, I=0, C=6

46. Interpolating currents Current for 5-quarks without derivative =(current for triquark)*(current for diquark) With A state : Two currents 0!

47. With B state : Energy dimension of correlator for the 5- quark after the Borel transform : 13 The 2 nd sum rule with massless u,d :

48. Sum rules by other authors 1.Shi-Lin Zhu, PRL91 (2003) 232002 : - Current : - Sum rule : 1 st sum rule up to d=12 - Mass ~1.56 GeV, Parity = ? 2. R. D. Matheus et al, PLB578(2004) 323 - Two currents : not proper for - Sum rule : 1 st sum rule up to d=12 - Mass~1.54, Parity = ?

49. 3. M. Eidelmuller, PLB 597 (2004) 314 - Current : P-wave current - Sum rule : 1 st sum rule up to d=6 - Mass~1.64, Parity = ? 4. J. Sugiyama et al, PLB 581 (2004) 167 - Current : - Sum rule : Both sum rules up to d=6 - Mass~1.63, Parity = -1 - Current is very similar to our A state

50. 2 nd sum rule for A up to d=13 : diagrammatic representation

51. Parameters in Matheus et al, hep-ph/0412063 LHS + or - ?

52. Left hand side (LHS) of 2 nd sum rule : Sign of LHS is changed with going from d=5 to d=7 : Parity of state is changed.

53. Contribution from Instanton Differently from model calculation, there is instanton effect in two quark pairs of only. No instanton effect in three quarks by the color- spin structure of the current!!! Instanton effect is small in

54. Mass fitting with Instanton

55. Final summary For parity : higher operators are important since correlator of Pentaquark has higher energy dimension. Instanton effect is unexpectively small Mass is around 1.75MeV + parity : one quark is in excited state? Two clusters in L=1? B state in the triquark cluster?