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 KEK seminar 12 May 2005

Preliminary T.Nakano et al. (LEPS Collab.) Phys. Rev. Lett. 91 (2003) 012002 Laser-Electron Photon facility @ SPring-8 KEK seminar 12 May 2005

Contents Introduction Lattice study for penta-quarks Our strategy Lattice results Conclusion & Outlook Some remarks KEK seminar 12 May 2005

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 ! KEK seminar 12 May 2005

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

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

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] KEK seminar 12 May 2005

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

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

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

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

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

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 KEK seminar 12 May 2005

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

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

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

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

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

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

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

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

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

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

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

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

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

boundary condition Periodic/anti-periodic boundary for quarks meff  EN-EK _ Dirichlet boundary  no problem KEK seminar 12 May 2005

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

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

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