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Lattice study for penta-quark states

Lattice study for penta-quark states. T. Umeda with T.T.Takahashi,T.Onog,T.Kunihiro (YITP, Kyoto University). hep-lat/0503019. KEK seminar 12/May/2005. Preliminary. T.Nakano et al. (LEPS Collab.) Phys. Rev. Lett. 91 (2003) 012002 Laser-Electron Photon facility @ SPring-8. Contents.

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Lattice study for penta-quark states

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  1. Lattice study for penta-quark states T.Umeda with T.T.Takahashi,T.Onog,T.Kunihiro (YITP, Kyoto University) hep-lat/0503019 KEK seminar12/May/2005

  2. Preliminary T.Nakano et al. (LEPS Collab.) Phys. Rev. Lett. 91 (2003) 012002 Laser-Electron Photon facility @ SPring-8

  3. Contents • Introduction • Lattice study for penta-quarks • Our strategy • Lattice results • Conclusion & Outlook • Some remarks

  4. Introduction • Baryon with Positive strangeness Minimal quark content is 5 quarks • Very narrow width • Mass = 1539.2±1.6MeV (NK ≈ 1435MeV) • Spin & parity are not determined • Existence is not conclusive yet !

  5. Experiments • LEPS Collab. [Phys.Rev.Lett.91(2003)012002] • DIANA Collab. [Phys.Atom.Nucl.66(2003)1715] • CLAS Collab. [Phys.Rev.Lett.91(2003)252001] [Phys.Rev.Lett.92(2004)032001] • SAPHIR Collab. [Phys.Lett.B572(2003)127] • ZEUS Collab. [Phys.Lett.B591(2004)7] • A.E.Asratyan et al. [Phys.Atom.Nucl.67(2004)682] • HERMES Collab. [Phys.Lett.B585(2004)213] • COSY-TOF Collab. [Phys.Lett.B595(2004)127] No Θ+ in high energy experiments ?

  6. Theories Some models • Chiral soliton model (Skyrme model) • Quark model • ... Studies based on QCD • QCD sum rule • Lattice QCD It is possible to study hadrons from first principles.

  7. Lattice studies • F.Csikor et al. [JHEP0311(03)070] [hep-lat/0503012] • S.Sasaki [Phys.Rev.Lett.93(2004)152001] • T.W.Chiu et al. [hep-ph/0403020] • N.Mathur et al. [Phys.Rev.D70(2004)074508] • N.Ishii et al. [Phys.Rev.D71(2005)034001] • B.G.Lasscock et al. [hep-lat/0503008] • C.Alexandrou, A.Tsapalis [hep-lat/0503013] • T.T.Takahashi et al. [hep-lat/0503019]

  8. Lattice studies Hadron spectrum from first principles • dynamical quark effects (Nf=2+1) • infinite volume limit • chiral extrapolation • continuum limit Depending on our purpose we can compromise some of them

  9. Difficulties for Θ+ on the lattice Correlation function of hadronic op. • Θ+is not a lowest-state in this channel we have to extract 2 states at lease • Θ+has the same quantum number as KN states we have to distinguish from KN states • discretized lattice momenta in a finite box dilemma of spatial volume

  10. Our strategy It would be premature to study penta-quarks on lattice quantitatively ! • give up a quantitative study △ course lattice, no cont. limit, quench ○ high statistics (1K~3K confs.) • extract lowest two states using 2x2 correlation matrices • distinguish Θ+ from KN states volume dependence (V=83~163) of mass & spectral weight

  11. Lattice studies

  12. Interpolating operators I=0, J=1/2 channel Nucleon x Kaon operator Penta-quark like operator Same as Csikor et al. (other op.  Some remarks)

  13. Simulation parameters Wilson quark & Plaquette gauge beta=5.7 (a~0.2fm), quenched QCD 83x24 [(1.6fm)3x4.8fm] 3000confs. 103x24 [(2.0fm)3x4.8fm] 2900confs. 123x24 [(2.4fm)3x4.8fm] 1950confs. 163x24 [(3.2fm)3x4.8fm] 950conf. 5 combinations of quark mass = (100~240MeV) (mpi/mrho=0.65~0.85) Done on SX-5 @ RCNP & SR8000 @ KEK

  14. Quality of data (I, JP) = (0, 1/2—)

  15. Quality of data (I, JP) = (0, 1/2—)

  16. Volume dependence (I, JP) = (0, 1/2—)

  17. Volume dependence (I, JP) = (0, 1/2—)

  18. NK scattering state (I, JP) = (0, 1/2—) (1) Naive expectation Nucl. & Kaon with a relative mom. p=2pi/L small/neglegible interaction (1’) Nucleon with non-zero momentum + Kaon with non-zero momentum (2) Effects of interacton Luscher’s formula + scatt. length (exp.)  a few % deviation

  19. Volume dependence (I, JP) = (0, 1/2—)

  20. Volume dependence (I, JP) = (0, 1/2—)

  21. Volume dependence (I, JP) = (0, 1/2—) heavier quark mass smaller error rather compact interaction ? 2nd lowest state may be resonance state !

  22. Spectral weight (I, JP) = (0, 1/2—) overlap of local operator with each state relative wavefunc. between N and K resonance state has small volume dep. volume of the system

  23. Spectral weight (I, JP) = (0, 1/2—) lowest-state expected to be NK scatt. with rela. mom. p=0  1/V dependence 2nd lowest-state expected to be resonance state  no V dependence L=10,12,14 and 16 are used

  24. Positive parity (I, JP) = (0, ½+) (u,d,s)=(240,240,240)MeV N*+K mass spectrum no L dependence far from NK threshold spectral weight 1/V dependence  only scattering state  Small L Large L 

  25. Summary & Conclusion We study a penta-quark state with (I,J)=(0,1/2) Our aim isTheta+ exists or not on the lattice? • extract lowest two states • examine the volume dependence of mass & spectral weight Conclusion: resonance state is likely to exist slightly above the NK threshold in (I,JP)=(0,1/2-)

  26. Future plans • Estimation of the width using level crossing Soft pion theorem + ChPT • Wave function B-S amplitude of KN state • Full QCD simulation using CP-PACS config. Nf=2, cont. limit no volume dep.

  27. _ meff EN-EK boundary condition • Periodic/anti-periodic boundary for quarks • Dirichlet boundary  no problem

  28. Operator dependences • NK like op. (wall source) • Penta like op. (wall source) • NK like op. (point source) • Penta like op. (point source) • Di-quark like op. (point source) small spin&color structure dependence large spatial structure dependence local op. ~ Penta., extended op. ~ NK scatt.

  29. Other studies

  30. Chiral extrapolation MK=0.5001(14) GeV, MN=0.9355(70) GeV MTheta+=1.755(61) GeV (163x24 data, 1/a by Mrho, ms by Kaon)

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