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Pentaquark Baryons and Tetraquark Mesoniums from Lattice QCD

Pentaquark Baryons and Tetraquark Mesoniums from Lattice QCD . Hadron Calculation with overlap fermion Pentaquark Baryons and Tetraquark Mesoniums on the Lattice . χ QCD Collaboration : A. Alexandru, Y. Chen, S.J. Dong, T. Draper, I. Horvath, B. Joo,

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Pentaquark Baryons and Tetraquark Mesoniums from Lattice QCD

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  1. Pentaquark Baryons and Tetraquark Mesoniums from Lattice QCD • Hadron Calculation with overlap fermion • Pentaquark Baryons and Tetraquark Mesoniums on the Lattice χQCDCollaboration: A. Alexandru, Y. Chen, S.J. Dong, T. Draper, I. Horvath, B. Joo, F .X. Lee, K.F. Liu, N. Mathur, S. Tamhankar, H.Thacker, J.B. Zhang Charm 2006, June 6, 2006

  2. Hadron Mass and Decay Constant The two-point Green’s function decays exponentially at large separation of time Mass M= Ep(p=0), decay constant ~ Φ

  3. QCD Vacuum

  4. ρ π Ξ φ Λ σ Σ N Δ ω * N K S11 Creation Operator QCD Vacuum

  5. Θ+ ?? ?? Tetraquark Pentaquark Creation Operator QCD Vacuum

  6. Le Taureau of Pablo Picasso (1945) 5thstage 11th stage Dynamical chiral fermion Quenched approximation with chiral symmetry, and light quark masses

  7. Masses of N, ρ, and π • 163 x 28 quenched lattice, Iwasaki action with a = 0.200(3) fm • Overlap fermion • Critical slowing down is gentle • Smallest mπ~ 180 MeV • mπL > 3

  8. Evidence of η’N GHOST State in S11 (1535) Channel η η - - - - W > 0 W<0

  9. u d d u Possible Pentaquark candidate Possible candidate Signal reported to be “observed” recently θ+(1540)

  10. N K N K d d u u d d u u u u d d d d u u 1) Need to discern the nature of the states mK+ mN ~ 1432 MeV m(Θ+) ~1540MeV ٭Not sufficient to study the masses/energies of the states, particularly in the 1/2- channel. ٭Volume study of spectral weight W is much more sensitive.

  11. Lattice Results on Θ+ Pentaquark Lattice Pentaquark Volume Variational Light enough Ghost Group signal claim Test Calculation Quark Mass State Csikor YesNo Yes (2) No No et.al No No Yes (9/6) No No Sasaki Yes No No No No Chiu et.alYes NoYes No No Mathur et.alNo Yes No Yes Yes Ishii et.al NoYes No No No AlexandrouYesYes No No No TakahashiYesYes Yes(2) No No Negele et.al ? Yes Yes(19) Lasscock et. al NoNoNo No No Holland et. al No No Yes No No

  12. Status of Lattice Pentaquark CalculationKFL and N. Mathur (hep-lat/0510036) • No convincing evidence for the claims of observing pentaquarks on the lattice. • Absence of evidence is not evidence of absence. • Definite calculation should involve dynamic chiral fermion with light quarks, variational approach, volume test, and removal of ghosts.

  13. q1 q2 Tetraquark Mesoniums QCD allows a state with more than three quarks Four quarks : Two quarks + two anti-quarks Like molecular state? Like di-quark anti-diquark state?

  14. f0(1710) f0(1500) a0(1450) K0*(1430) f0(1370) a2(1320) a1(1230) a0(980) f0(980) M (MeV) ρ(770) K0*(800) σ(600) π(137) JPG(I)) 1+ ¯(1) 0¯ ¯(1) 2+ ¯(1) 0+¯(1) 0++(0) 0+(1/2) 1¯+(1)

  15. Is a0 (1450) (0++) a two quark state? Correlation function for Scalar channel Ground state : πηghost state. First excited state : a0

  16. ms Our results shows scalar mass around 1400-1500 MeV, suggesting a0(1450)is a two quark state.

  17. Two-pion exchange potential: Chembto, Durso, Riska; Stony Brook, Paris, … σ (500): Johnson and Teller σ enhancement of Δ I = ½ rule What is the nature of σ (600)?

  18. Without a σ pole σ With a σ pole The σ in D+→π¯π+π+ Mσ= 478 ± 2423± 17MeV Γσ= 324 ± 4240 ± 21 MeV E.M. Aitala et. al. Phys. Rev. Lett. 86, 770, (2001)

  19. J/ψ—> ωπ+π- M. Ablikim et al. (BES), Phys. Lett. B598, 149 (2004) Mσ= 541 ± 39 MeV, Γσ= 504 ± 84 MeV

  20. ππfour quark operator (I=0)

  21. Scattering Length and energy shift • ππenergies : • Threshold energy shift on the finite lattice:

  22. Scattering states Possible BOUND state σ(600)? Scattering states (Negative scattering length) Further study is needed to check the volume dependence of the observed states.

  23. Scattering state and its volume dependence Normalization condition requires : Continuum Two point function : Lattice For one particle bound state spectral weight (W) will NOT be explicitly dependent on lattice volume

  24. Scattering state and its volume dependence Normalization condition requires : Continuum Two point function : Lattice For two particle scattering state spectral weight (W) WILL be explicitly dependent on lattice volume

  25. Volume dependence of spectral weights Preliminary W0 W1 Volume independence suggests the observed state is an one particle state

  26. f0(1710) f0(1500) a0(1450) K0*(1430) f0(1370) a2(1320) a1(1230) a0(980) f0(980) M (MeV) ρ(770) K0*(800) σ(600) Kπ Mesonium ππMesonium π(137) JPG(I)) 1+ ¯(1) 0¯ ¯(1) 2+ ¯(1) 0+¯(1) 0++(0) 0+(1/2) 1¯+(1)

  27. Mixing of First order approximation: exact SU(3) x is annihilation diagram

  28. Mixing of with Glueball First order approximation: exact SU(3)

  29. Scalar Mesons and Glueball glueball

  30. Summary • No credible evidence of pentaquarks in lattice calculations • Plenty of tetraquark mesonium candidates • σ(600) is very likely to be a tetraquark mesonium. • Pattern of light scalar mesons may be repeated in the heavy-light sectors (?)

  31. Azimuthal anisotropy in Au + Au collisions with = 200 GeV (STAR collaboration)

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