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KEK seminar 12 May Lattice study for penta-quark states T. Umeda with T.T.Takahashi,T.Onog,T.Kunihiro (YITP, Kyoto University) KEK seminar 12/May/2005 hep-lat/

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KEK seminar 12 May Preliminary T.Nakano et al. (LEPS Collab.) Phys. Rev. Lett. 91 (2003) Laser-Electron Photon SPring-8

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KEK seminar 12 May Contents Introduction Lattice study for penta-quarks Our strategy Lattice results Conclusion & Outlook Some remarks

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KEK seminar 12 May Introduction Baryon with Positive strangeness Minimal quark content is 5 quarks Very narrow width Mass = ± 1.6MeV (NK ≈ 1435MeV) Spin & parity are not determined Existence is not conclusive yet !

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KEK seminar 12 May 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 ?

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KEK seminar 12 May 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.

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KEK seminar 12 May Lattice studies F.Csikor et al. [JHEP0311(03)070] [hep-lat/ ] S.Sasaki [Phys.Rev.Lett.93(2004)152001] T.W.Chiu et al. [hep-ph/ ] 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/ ] C.Alexandrou, A.Tsapalis [hep-lat/ ] T.T.Takahashi et al. [hep-lat/ ]

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KEK seminar 12 May Lattice studies Hadron spectrum from first principles dynamical quark effects (N f =2+1) infinite volume limit chiral extrapolation continuum limit Depending on our purpose we can compromise some of them

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KEK seminar 12 May 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

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KEK seminar 12 May Our strategy 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=8 3 ~16 3 ) of mass & spectral weight It would be premature to study penta-quarks on lattice quantitatively !

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KEK seminar 12 May Lattice studies signalParitydiag.V dep. Csikor et al. (1)Yesnegative× △ S.SasakiYesnegative×× Kentuchy groupNon/a× △ TITECH groupNon/aHB× Chiu & HsiehYespositive ○ × Lasscock et al.No(*)n/a △ × Csikor et al. (2)Non/a ○○ Alexandrou et al.Yesnegative ○○ YITPYesnegative ○○

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KEK seminar 12 May 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)

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KEK seminar 12 May Simulation parameters Wilson quark & Plaquette gauge beta=5.7 (a~0.2fm), quenched QCD 8 3 x24 [(1.6fm) 3 x4.8fm] 3000confs x24 [(2.0fm) 3 x4.8fm] 2900confs x24 [(2.4fm) 3 x4.8fm] 1950confs x24 [(3.2fm) 3 x4.8fm] 950conf. 5 combinations of quark mass = (100~240MeV) (m pi /m rho =0.65~0.85) Done on RCNP & KEK

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KEK seminar 12 May Quality of data (I, J P ) = (0, 1/2 — )

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KEK seminar 12 May Quality of data (I, J P ) = (0, 1/2 — )

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KEK seminar 12 May Volume dependence (I, J P ) = (0, 1/2 — )

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KEK seminar 12 May Volume dependence (I, J P ) = (0, 1/2 — )

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KEK seminar 12 May NK scattering state (I, J P ) = (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

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KEK seminar 12 May Volume dependence (I, J P ) = (0, 1/2 — )

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KEK seminar 12 May Volume dependence (I, J P ) = (0, 1/2 — )

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KEK seminar 12 May Volume dependence (I, J P ) = (0, 1/2 — ) 2nd lowest state may be resonance state ! heavier quark mass smaller error rather compact interaction ?

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KEK seminar 12 May Spectral weight (I, J P ) = (0, 1/2 — ) volume of the system overlap of local operator with each state relative wavefunc. between N and K resonance state has small volume dep.

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KEK seminar 12 May Spectral weight (I, J P ) = (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

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KEK seminar 12 May Positive parity (I, J P ) = (0, ½ + ) Small L Large L (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

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KEK seminar 12 May Summary & Conclusion We study a penta-quark state with (I,J)=(0,1/2) Our aim is Theta+ 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,J P )=(0,1/2 - )

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KEK seminar 12 May 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. N f =2, cont. limit no volume dep.

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KEK seminar 12 May boundary condition Periodic/anti-periodic boundary for quarks m eff E N -E K _ Dirichlet boundary no problem

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KEK seminar 12 May 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.

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KEK seminar 12 May Other studies signalParitydiag.V dep. Csikor et al. (1)Yesnegative× △ S.SasakiYesnegative×× Kentuchy groupNon/a× △ TITECH groupNo(*)n/aHB× Chiu & HsiehYespositive ○ × Lasscock et al.No(*)n/a △ × Csikor et al. (2)Non/a ○ ○ (*) Alexandrou et al.Yesnegative ○ (*) ○ YITPYesnegative ○○

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KEK seminar 12 May Chiral extrapolation M K =0.5001(14) GeV, M N =0.9355(70) GeV M Theta +=1.755(61) GeV (16 3 x24 data, 1/a by M rho, m s by Kaon)

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