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Inter-Quark Potentials in Baryons and Multi-Quark Systems in QCD

Inter-Quark Potentials in Baryons and Multi-Quark Systems in QCD. H. Suganuma, A. Yamamoto, H. Iida, N. Sakumichi (Kyoto Univ.) with T.T.Takahashi (Kyoto Univ.), F. Okiharu (Nihon U.). Contents 1. Three-Quark Potential in SU(3) lattice QCD 2. Multi-Quark Potential in SU(3) lattice QCD

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Inter-Quark Potentials in Baryons and Multi-Quark Systems in QCD

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  1. Inter-Quark Potentials in Baryons and Multi-Quark Systems in QCD H. Suganuma, A. Yamamoto, H. Iida, N. Sakumichi (Kyoto Univ.) with T.T.Takahashi (Kyoto Univ.), F. Okiharu (Nihon U.) Contents 1. Three-Quark Potential in SU(3) lattice QCD 2. Multi-Quark Potential in SU(3) lattice QCD 3. Heavy-heavy-light quark potential and Light-quark effects to the inter-two-quark interaction in baryons (SU(3) lattice QCD and Analytical model calculation) Chiral 07, Nov 13-16 2007, RCNP Osaka

  2. Inter-quark potential in QCD In 1979, M.Creutz performed the first application of lattice QCD simulation for the quark-antiquark potential using the Wilson loop. Since then, the study of the inter-quark force has been one of the central issues in lattice QCD. Actually, in hadron physics, the inter-quark force can be regarded as an elementary quantity to connect the “quark world” to the “hadron world”, and plays an important role to hadron properties. In 1999, in addition to the quark-antiquark potential, we performed the first accurate reliable lattice QCD study for the three-quark (3Q) potential, which is responsible to the baryon structure at the quark-gluon level. Furthermore, in 2005, we performed the first lattice QCD study for the multi-quark potentials, i.e., 4Q and 5Q potentials, which give essential information for the multi-quark hadron physics. Note also that the study of 3Q and multi-quark potentials is directly related to the quark confinement properties in baryons and multi-quark hadrons. First, I review the lattice QCD results for static inter-quark potentials.

  3. Quark-antiquark static potential in Lattice QCD M.Creutz (1979,80) quark anti-quark r t T Wilson loop The quark-antiquark potential can be obtained from the Wilson Loop.

  4. Quark-antiquark static potential in Lattice QCD M.Creutz (1979,80) Summarized lattice QCD data G.S.Bali (2001) Takahashi, H.S. et al. (2002) JLQCD (2003) quark anti-quark r0=0.5fm:unit r t T Wilson loop 1 T The quark-antiquark potential can be obtained from the Wilson Loop. V(r) = －lim ln<W>T T→∞

  5. Quark-antiquark static potential in Lattice QCD M.Creutz (1979,80) Summarized lattice QCD data G.S.Bali (2001) Takahashi, H.S. et al. (2002) JLQCD (2003) quark anti-quark r0=0.5fm:unit g2 3π 1 r V(r) = － +σr The quark-antiquark potential V(r) is well described by Coulomb + Linear Potential. σ≒ 0.89 GeV/fm

  6. Quark-antiquark static potential in Lattice QCD M.Creutz (1979,80) Summarized lattice QCD data G.S.Bali (2001) Takahashi, H.S. et al. (2002) JLQCD (2003) quark anti-quark r0=0.5fm:unit g2 3π 1 r V(r) = － +σr quark anti-quark － At the short distances, the Q-Q potential behaves as the Coulomb-type potential, which is expected from the one-gluon-exchange (OGE) process. g g

  7. Quark-antiquark static potential in Lattice QCD M.Creutz (1979,80) Summarized lattice QCD data G.S.Bali (2001) Takahashi, H.S. et al. (2002) JLQCD (2003) quark anti-quark r0=0.5fm:unit At the long distances, the Q-Q potential behaves as a linear arising potential like a “condenser”, which indicates one-dimensional squeezing of the color-electric flux between quark and antiquark. － g2 3π 1 r V(r) = － +σr

  8. Quark-antiquark static potential in Lattice QCD M.Creutz (1979,80) Summarized lattice QCD data G.S.Bali (2001) Takahashi, H.S. et al. (2002) JLQCD (2003) quark anti-quark r0=0.5fm:unit r t g2 3π 1 r V(r) = － +σr T Wilson loop quark anti-quark － One-dimensional squeezing of color flux between q and q g g anti-quark quark

  9. Baryonic Three-Quark Potential in Lattice QCD quark quark What Shape of Color Flux? Confining Force? quark Before our study, there was almost No lattice QCD study for the Three-Quark Potential. This is not so trivial especially for quark confining force in baryons at long distance.

  10. PRThis is the cover of a recent textbook written by Hosaka and Toki.

  11. PRThis is the cover of a recent textbook written by Hosaka and Toki. This is a nice textbook for the introduction to quark-hadron physics

  12. PRThis is the cover of a recent textbook written by Hosaka and Toki. But! Look! Is this a correct picture for the color flux tube inside baryons ?

  13. Systematical Studies for Three and Multi-Quark Potentials in Lattice QCD “Detailed Analysis of Tetraquark Potential and Flip Flop in SU(3) Lattice QCD”F. Okiharu, H. Suganuma and T.T. Takahashi Physical Review D72 (2005) 014505 (17 pages). “First Study for the Pentaquark Potential in SU(3) Lattice QCD”F. Okiharu, H. Suganuma and T.T. Takahashi Physical Review Letters 94 (2005) 192001 (4 pages). “Detailed Analysis of the Gluonic Excitation in the 3Q System in Lattice QCD”T.T. Takahashi and H. Suganuma Physical ReviewD70 (2004) 074506 (13 pages). “Gluonic Excitation of the Three-Quark System in SU(3) Lattice QCD”T.T. Takahashi and H. Suganuma Physical Review Letters 90 (2003) 182001 (4 pages). “Detailed Analysis of the Three Quark Potential in SU(3) Lattice QCD”T.T. Takahashi, H. Suganuma et al. Physical ReviewD65 (2002) 114509 (19 pages). “Three-Quark Potential in SU(3) Lattice QCD”T.T. Takahashi, H. Suganuma et al. Physical Review Letters 86 (2001) 18-21.

  14. t 1 T V3Q(r) =－limln<W3Q>T T→∞

  15. k j i (i, j, k) characterize the shape of the 3Q triangle.

  16. k j i (i, j, k) characterize the shape of the 3Q triangle.

  17. k j i (i, j, k) characterize the shape of the 3Q triangle.

  18. k j i (i, j, k) characterize the shape of the 3Q triangle.

  19. n k -m l (l, m, n) characterize the shape of another type of 3Q triangles. j i (i, j, k) characterize the shape of the 3Q triangle. More than 300 different shapes of 3Q triangles are analyzed in total.

  20. quark quark color electric flux quark Lmin：total length of string linking three valence quarks

  21. Takahashi, H.S. et al. PRL 86 (2001) 18 Takahashi, H.S. et al.PRD65 (2002)114509 Takahashi, H.S. PRL 90 (2003) Takahashi, H.S.PRD70 (2004) 074506 Okiharu, H.S. et al. PRD72 (2005) 014505 Baryonic Three-Quark Potential in Lattice QCD quark quark What Shape of Color Flux? Confining Force? quark Before our study, there was almost No lattice QCD study for the Three-Quark Potential

  22. quark quark color electric flux quark Takahashi, H.S. et al. PRL 86 (2001) 18 Takahashi, H.S. et al.PRD65 (2002)114509 Takahashi, H.S. PRL 90 (2003) Takahashi, H.S.PRD70 (2004) 074506 Okiharu, H.S. et al. PRD72 (2005) 014505 Baryonic Three-Quark Potential in Lattice QCD conf V3Q(r)

  23. Takahashi, H.S. et al. PRL 86 (2001) 18 Takahashi, H.S. et al.PRD65 (2002)114509 Takahashi, H.S. PRL 90 (2003) Takahashi, H.S.PRD70 (2004) 074506 Okiharu, H.S. et al. PRD72 (2005) 014505 Baryonic Three-Quark Potential in Lattice QCD conf V3Q(r) quark quark color electric flux quark Lmin：total length of string linking three valence quarks g2 4π 3 TiaTja |ri - rj| V3Q(r) = ∑ + σLmin i<j One-Gluon-Exchange Coulomb potential Linear potential based on string picture

  24. Lattice QCD result for Color Flux-Tube Formation in baryons H. Ichie et al., Nucl. Phys. A721, 899 (2003)

  25. The status of our studies of 3Q potential Our studies of the 3Q potential are introduced as “one whole subsection” with citing 4 our papers in 3rd edition of “Lattice Gauge Theories”, which is one of the most popular lattice QCD text books.

  26. PRThis is the cover of a recent textbook written by Hosaka and Toki. ?

  27. PRThis is the cover of a recent textbook written by Hosaka and Toki. I have corrected it with the appropriate picture for the color flux tube inside baryons.

  28. PRThis is the cover of a recent textbook written by Hosaka and Toki. Without a matter of the cover, this is a nice textbook for the introduction to quark-hadron physics. I have corrected it with the appropriate picture for the color flux tube inside baryons.

  29. PRThis is the cover of the proceedings of Confinement Conference.

  30. Multi-Quark Hadrons and Multi-Quark Potentials In these years, there have been reported experimental discoveries of several candidates of multi-quark hadrons such as Θ+(1530), X(3872) and so on. Very recently, the discovery of a “charged charmonium” Z+(4430) (ccud) is reported at KEK-Belle experiment. - -

  31. Tetra-Quark Z(4430) from KEK press release The charged charmonium Z+(4430) is a manifest Tetra-Quark hadron composed by ccud. - -

  32. Multi-Quark Hadrons and Multi-Quark Potentials In these years, there have been reported experimental discoveries of several candidates of multi-quark hadrons such as Θ+(1530), X(3872) and so on. Very recently, the discovery of a “charged charmonium” Z+(4430) (ccud) is reported at KEK-Belle experiment. For the quark-model calculation of the multi-quark system, it is rather important to clarify the multi-quark potential, which gives the quark-model Hamiltonian for multi-quark system. In fact, the quark model analysis with appropriate multi-quark potential clarifies whether each exotic hadron exists or not, gives the properties of multi-quark hadrons, and predicts new-type exotic hadrons theoretically. We perform first study of multi-quark potential in lattice QCD. - -

  33. First Lattice QCD Study for Static Quark Potential in Multi-Quark System Okiharu, H.S. et al. PRL 94 (2005) 192001 Okiharu, H.S. et al. PRD72 (2005) 014505 anti-quark quark ? 4 quark system quark anti-quark What Shape of Color Flux? Confining Force?

  34. First Lattice QCD Study for Static Quark Potential in Multi-Quark System Okiharu, H.S. et al. PRL 94 (2005) 192001 Okiharu, H.S. et al. PRD72 (2005) 014505 What Shape of Color Flux? Confining Force? quark quark ? 5 quark system anti-quark quark quark

  35. First Lattice QCD Study for Static Quark Potential in Multi-Quark System Okiharu, H.S. et al. PRL 94 (2005) 192001 Okiharu, H.S. et al. PRD72 (2005) 014505 We formulate Multi-Quark Wilson Loops. anti-quark quark 4 quark system quark anti-quark 4 Quark Wilson Loop quark quark 5 quark system anti-quark quark quark 1 T VNQ(r) =－limln<WNQ>T 5 Quark Wilson Loop T→∞ The Multi-Quark potentials can be obtained from the corresponding Multi-Quark Wilson Loops.

  36. First Lattice QCD Study for Static Quark Potential in Multi-Quark System Okiharu, H.S. et al. PRL 94 (2005) 192001 Okiharu, H.S. et al. PRD72 (2005) 014505 anti-quark quark 4 quark system VNQ(r) quark anti-quark N=4,5 quark quark 5 quark system anti-quark quark quark Partial lattice QCD data of Multi-quark potential For more than 200 different patterns of multi-quark configurations, we have accurately performed the first lattice QCD calculations for multi-quark potentials.

  37. First Lattice QCD Study for Static Quark Potential in Multi-Quark System Okiharu, H.S. et al. PRL 94 (2005) 192001 Okiharu, H.S. et al. PRD72 (2005) 014505 anti-quark quark 4 quark system VNQ(r) quark anti-quark N=4,5 color flux tube quark quark 5 quark system anti-quark quark quark Partial lattice QCD data of Multi-quark potential For more than 200 different patterns of multi-quark configurations, we have accurately performed the first lattice QCD calculations for multi-quark potentials.

  38. First Lattice QCD Study for Static Quark Potential in Multi-Quark System Okiharu, H.S. et al. PRL 94 (2005) 192001 Okiharu, H.S. et al. PRD72 (2005) 014505 anti-quark quark 4 quark system VNQ(r) quark anti-quark N=4,5 color flux tube quark quark 5 quark system anti-quark quark quark Partial lattice QCD data of Multi-quark potential For more than 200 different patterns of multi-quark configurations, we have accurately performed the first lattice QCD calculations for multi-quark potentials.

  39. First Lattice QCD Study for Static Quark Potential in Multi-Quark System Okiharu, H.S. et al. PRL 94 (2005) 192001 Okiharu, H.S. et al. PRD72 (2005) 014505 anti-quark quark 4 quark system VNQ(r) quark anti-quark N=4,5 color flux tube quark quark 5 quark system anti-quark quark quark Lmin：total length of string linking the N valence quarks g2 4π N TiaTja |ri - rj| VNQ(r) = ∑ + σLmin i<j One-Gluon-Exchange Coulomb potential Linear potential based on string picture

  40. Okiharu, H.S. et al. PRD72 (2005) 014505 h 2d

  41. Summary of the First Part ~Static Potentials~ We have performed the first accurate Lattice QCD studies for static multi-quark (3Q, 4Q, 5Q) potentials. The multi-quark potential is well described by OGE Coulomb+ String-picture Linear Confinement Potential. Lmin：total length of string linking the N valence quarks g2 4π N TiaTja |ri - rj| VNQ(r) = ∑ + σLmin i<j One-Gluon-Exchange Coulomb potential Linear potential based on string picture We have found theUniversality of Quark Confinement Force (String Tension) in hadrons:σQQ =σ3Q =σ4Q =σ5Q -

  42. Heavy-Heavy-Light Quark Potential and Light-quark Effects to Inter-two-quark Interaction in Baryons~SU(3) Lattice QCD and Analytical Model Calculation~ So far, we have obtained the definite conclusions for the static inter-quark potentialsin QCD. However, in the real world,the quark mass is finite and quarks are moving inside hadrons. Here, we investigate the effect of the quark motion to the inter-two-quark interaction in baryons. To this end, we study the idealized situation of heavy-heavy-light quark systems where two heavy quarks can be treated as static quarks. So far, we have obtained the definite conclusions for the static inter-quark potentialsin QCD. However, in the real world,the quark mass is finite and quarks are moving inside hadrons. Here, we investigate the effect of the quark motion to the inter-two-quark interaction in baryons. To this end, we study the idealized situation of heavy-heavy-light quark systems (QQq systems) where two heavy quarks can be treated as static quarks. This situation physically corresponds to “doubly charmed baryon” as . idealize static quarks

  43. Mass : 3519 ± 1 MeV Doubly charmed baryon In 2002, the first doubly charmedbaryon was experimentally observed at SELEX, Fermilab. M. Mattson et al., Phys. Rev. Lett. 89, 112001 (2002). A. Ocherashvili et al., Phys. Rev. Lett. B628, 18 (2005). Theoretical calculations for the doubly charmed baryons Lattice QCD : R. Lewis et al., Phys. Rev. D 64, 094509 (2001). N. Mathur et al., Phys. Rev. D 66, 014502 (2002). Potential model : A. D. Rujula et al., Phys. Rev. D 12, 147 (1975).

  44. Doubly charmed baryon (experiment) The first experimental observation at SELEX, Fermilab 600 GeV/c charged hyperon beam Mass 3519 ± 1 MeV/c 2 M. Mattson et al., Phys. Rev. Lett. 89, 112001 (2002).

  45. W. M. Yao et al., J. Phys. G 33, 1 (2006).

  46. W. M. Yao et al., J. Phys. G 33, 1 (2006).

  47. R R Heavy-heavy-light quark (QQq) potential The situation is idealized as Two heavy quarks (Q) → Twostatic quarks (MQ→∞) One light quark (q) → finite-mass quark (Mq: various value) The QQq potential VQQq(R) is defined as the energy of QQq systems in terms of the inter-heavy-quark distance R. One light quark is moving around Two Static Quarks We calculate the QQq potentialVQQq(R)in Lattice QCD and also in a non-relativistic potential model.

  48. QQq potential in Lattice QCD The QQq Wilson loop is defined as :light-quarkpropagator The QQq potential is obtained as cf) 3Q Wilson loop for static 3Q potential

  49. Lattice QCD Simulation Conditions • Standard plaquette gauge action • β= 6.0 (lattice spacing a=0.10 fm) • 164isotropic lattice • Quenched calculation • O(a)-improved clover fermion action • κ=0.1200, 0.1300, 0.1340, 0.1380 • Wall-source wall-sink propagator • Calculated on NEC-SX8R at RCNP, Osaka Univ. Constituent quark mass: Mq = mρ/2

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