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** Lattice study for penta-quark states**

T. Umeda with T.T.Takahashi,T.Onog,T.Kunihiro (YITP, Kyoto University) hep-lat/ KEK seminar 12/May/2005 KEK seminar 12 May 2005

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**Preliminary T.Nakano et al. (LEPS Collab.)**

Phys. Rev. Lett. 91 (2003) Laser-Electron Photon SPring-8 KEK seminar 12 May 2005

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**Contents Introduction Lattice study for penta-quarks Our strategy**

Lattice results Conclusion & Outlook Some remarks KEK seminar 12 May 2005

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**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 ! KEK seminar 12 May 2005

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**Experiments No Θ+ in high energy 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 ? KEK seminar 12 May 2005

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**It is possible to study hadrons**

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. KEK seminar 12 May 2005

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**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/ ] 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/ ] KEK seminar 12 May 2005

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**Hadron spectrum from first principles**

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 KEK seminar 12 May 2005

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**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 KEK seminar 12 May 2005

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**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 KEK seminar 12 May 2005

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**Lattice studies signal Parity diag. V dep. Csikor et al. (1) Yes**

negative × △ S.Sasaki Kentuchy group No n/a TITECH group HB Chiu & Hsieh positive ○ Lasscock et al. No(*) Csikor et al. (2) Alexandrou et al. YITP KEK seminar 12 May 2005

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**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) KEK seminar 12 May 2005

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**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 RCNP & KEK KEK seminar 12 May 2005

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Quality of data (I, JP) = (0, 1/2—) KEK seminar 12 May 2005

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Quality of data (I, JP) = (0, 1/2—) KEK seminar 12 May 2005

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Volume dependence (I, JP) = (0, 1/2—) KEK seminar 12 May 2005

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Volume dependence (I, JP) = (0, 1/2—) KEK seminar 12 May 2005

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**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 KEK seminar 12 May 2005

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Volume dependence (I, JP) = (0, 1/2—) KEK seminar 12 May 2005

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Volume dependence (I, JP) = (0, 1/2—) KEK seminar 12 May 2005

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**Volume dependence (I, JP) = (0, 1/2—) heavier quark mass smaller error**

rather compact interaction ? 2nd lowest state may be resonance state ! KEK seminar 12 May 2005

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**overlap of local operator with each state**

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 KEK seminar 12 May 2005

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**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 KEK seminar 12 May 2005

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**Positive parity (I, JP) = (0, ½+) N*+K mass spectrum no L dependence**

(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 KEK seminar 12 May 2005

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**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,JP)=(0,1/2-) KEK seminar 12 May 2005

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**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. KEK seminar 12 May 2005

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**boundary condition Periodic/anti-periodic boundary for quarks**

meff EN-EK _ Dirichlet boundary no problem KEK seminar 12 May 2005

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**Operator dependences small spin&color structure dependence**

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. KEK seminar 12 May 2005

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**Other studies signal Parity diag. V dep. Csikor et al. (1) Yes**

negative × △ S.Sasaki Kentuchy group No n/a TITECH group No(*) HB Chiu & Hsieh positive ○ Lasscock et al. Csikor et al. (2) ○(*) Alexandrou et al. YITP KEK seminar 12 May 2005

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**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) KEK seminar 12 May 2005

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