1. 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

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

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

4. 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

5. 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

6. 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

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/ ]
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

8. 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

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
KEK seminar 12 May 2005

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
KEK seminar 12 May 2005

11. 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

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)
KEK seminar 12 May 2005

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 RCNP & KEK
KEK seminar 12 May 2005

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

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

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

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

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
KEK seminar 12 May 2005

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

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

21. 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

22. 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

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
KEK seminar 12 May 2005

24. 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

25. 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

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.
KEK seminar 12 May 2005

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

28. 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

29. 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

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)
KEK seminar 12 May 2005