lattice study for penta-quark states

KEK seminar 12 May 2005 1

　 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/0503019


Preliminary

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


Contents

Introduction Lattice study for penta-quarks Our strategy Lattice results Conclusion & Outlook Some remarks


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 !


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 ?


Theories

Some models Chiral soliton model (Skyrme model) Quark model ... Studies based on QCD QCD sum rule Lattice QCD

It is possible to study hadronsfrom first principles.


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]


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


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


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=83~163) of mass & spectral weight

It would be premature to study penta-quarks on lattice quantitatively !


Lattice studies

signal Parity diag. V dep.

Csikor et al. (1) Yes negative × △S.Sasaki Yes negative × ×

Kentuchy group No n/a × △TITECH group No n/a HB ×Chiu & Hsieh Yes positive ○ ×Lasscock et al. No(*) n/a △ ×Csikor et al. (2) No n/a ○ ○Alexandrou et al. Yes negative ○ ○

YITP Yes negative ○ ○


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)


Simulation parameters

Wilson quark & Plaquette gaugebeta=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


Quality of data (I, JP) = (0, 1/2—)


Volume dependence (I, JP) = (0, 1/2—)


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



2nd lowest state may be resonance state !

heavier quark mass

smaller error

rather compact

interaction ?


Spectral weight (I, JP) = (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.


Spectral weight (I, JP) = (0, 1/2—)

lowest-stateexpected to be NK scatt. with rela. mom. p=0 1/V dependence

2nd lowest-stateexpected to be resonance state

no V dependence

L=10,12,14 and 16 are used


Positive parity (I, JP) = (0, ½+)

Small L Large L

(u,d,s)=(240,240,240)MeV

N*+K

mass spectrum no L dependence far from NK thresholdspectral weight 1/V dependence only scattering state


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-)


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.


boundary condition

Periodic/anti-periodic boundary for quarks

meff EN-EK _

Dirichlet boundary no problem


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 dependencelarge spatial structure dependencelocal op. ~ Penta., extended op. ~ NK scatt.


Other studies

signal Parity diag. V dep.

Csikor et al. (1) Yes negative × △

S.Sasaki Yes negative × ×

Kentuchy group No n/a × △

TITECH group No(*) n/a HB ×

Chiu & Hsieh Yes positive ○ ×

Lasscock et al. No(*) n/a △ ×

Csikor et al. (2) No n/a ○ ○(*)

Alexandrou et al. Yes negative ○(*) ○

YITP Yes negative ○ ○


Chiral extrapolation

MK=0.5001(14) GeV, MN=0.9355(70) GeVMTheta+=1.755(61) GeV

(163x24 data, 1/a by Mrho, ms by Kaon)

lattice study for penta-quark states

Documents

sasaki phys

lattice momenta

lattice studies f

clas collab

hermes collab

diana collab

saphir collab

experiments leps collab