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Lattice QCD study of the P E N T A quark baryons

Lattice QCD study of the P E N T A quark baryons. Toru T. Takahashi with Takashi Umeda, Tetsuya Onogi, Teiji Kunihiro. Yukawa Institute for Theoretical Physics. ・ Pentaquarks ・ Present lattice QCD studies of the pentaquarks ・ Ground state and 1 st excited state in I=0,J=1/2 channel

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Lattice QCD study of the P E N T A quark baryons

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  1. Lattice QCD study of the PENTA quark baryons Toru T. Takahashi with Takashi Umeda, Tetsuya Onogi, Teiji Kunihiro Yukawa Institute for Theoretical Physics ・Pentaquarks ・Present lattice QCD studies of the pentaquarks ・Ground state and 1st excited state in I=0,J=1/2 channel ・NK scattering state vs Pentaquark state ・Summary

  2. Θ+(1540) Pentaquarks B=1, S=+1  hypercharge Y=2 Minimal quark contents is5 quarks We find no Isospin-partners (Θ0Θ++) in experiments Isospin of the pentaquark is I=0 I=0, Y=2 Θ+(1540) should be a member of10*representation Has a very narrow width Spin and Parity remain undetermined!!

  3. R.A. Arndt, I.I. Strakovsky, R.L. Workman Phys.Rev.C68:042201,2003, Erratum-ibid.C69:019901,2004 J. Haidenbauer, G. Krein Phys.Rev.C68:052201,2003 ---- Theoretical studies of pentaquark baryons ---- Model calculations QCD-based studies Skyrme soliton model Quark model … QCD sum rule Lattice QCD study Reliable nonperturbative method based on QCD Pentaquarks spin? parity? Can pentaquark baryons exist………………? The width of Θ+ should be less than 1 MeV

  4. Present lattice QCD studies of the pentaquarks Rather controversial F.Csikor, Z.Fodor, F.Katz, T.Kovacs JHEP 0311 (03) 070 S.Sasaki hep-lat/0310014 Pentaquark state near KN threshold in negative parity channel Ting-Wai Chiu, Tung-Han Hsiehhep-lat/0403020, 0404007 Lowest lying Pentaquark is in positive parity channel N.Mathur et al. (Kentucky group)hep-ph/0406196 NO Pentaquark near KN threshold in both parity channel Titech group (Analysis using various boundary conditions) NO Pentaquark near KN threshold in both parity channel MIT group 4x4 correlation matrix ? We investigate the I=0, JP=1/2－, state using lattice QCD

  5. signal Energy of the ground state Ground state and 1st excited state in I=0,J=1/2 channel Difficulty in the lattice QCD calculation We suffer from the contaminations of the NK scattering state. Correlation between operators

  6. Ground state and 1st excited state in I=0,J=1/2 channel We need to separate each state. • We prepare two independent operators and make the correlation matrix and then diagonalize it to obtain the G.S and 1st E.S. : independent operators which couple to the same quantum number • Roughly speaking, we construct the operator which selectively couples to the n-th excited-state, from a linear combination of independent operators. T. T. T. and H. Suganuma Gluonic excitations in static three quark system Phys.Rev.Lett.90:182001,2003

  7. Many excited-state Only the ground-state Energy of the 1st E.S. Energy of the G.S. Ground state and 1st excited state in I=0,J=1/2 channel After the diagonalization…. Ground-state 1st excited-state

  8. Ground state and 1st excited state in I=0,J=1/2 channel Simulation conditions β=5.7 (lattice spacing : 0.2fm) quenched Wilson gauge action and Wilson quark action 83 x 24 [(1.6 fm)3 x 4.8fm] 3000 gauge configurations 103 x 24 [(2.0 fm)3 x 4.8fm] 2900 gauge configurations 123 x 24 [(2.4 fm)3 x 4.8fm] 1950 gauge configurations 163 x 24 [(3.2 fm)3 x 4.8fm] 950 gauge configurations Current quark mass : (u, d, s)～(240MeV, 240MeV, 240MeV) (100MeV, 100MeV, 240MeV) (240MeV, 240MeV, 100MeV) (100MeV, 100MeV, 100MeV) Done on SX5 at RCNP,Osaka University and SR8000 at KEK

  9. Ground state and 1st excited state in I=0,J=1/2 channel Interpolating operators Nucleaon Kaon N+K like operator Pentaquark like operator Same as Csikor et al. Spinor structure : same Color structure : different

  10. Ground state in (I, JP)=(0, 1/2-) channel

  11. NK scattering state vs Pentaquark state (u,d,s)=(100,100,100)MeV (u,d,s)=(100,100,240)MeV Mass (GeV)  Small L Large L   Small L Large L  1fm 2.4fm 4fm (u,d,s)=(240,240,240)MeV (u,d,s)=(240,240,100)MeV  Small L Large L   Small L Large L 

  12. NK scattering state vs Pentaquark state (u,d,s)=(100,100,100)MeV (u,d,s)=(100,100,240)MeV MN+MK Mass (GeV)  Small L Large L   Small L Large L  1fm 2.4fm 4fm (u,d,s)=(240,240,240)MeV (u,d,s)=(240,240,100)MeV  Small L Large L   Small L Large L 

  13. NK scattering state vs Pentaquark state Ground state in (I,J,P)=(0,1/2,-) channel  coincides with MN+MK  We find almost no volume dependence. It is expected to be the scattering state of Nucleon and Kaon, with the relative momentum p=0.

  14. 1st Excited state in (I, JP)=(0, 1/2-) channel

  15. NK scattering state vs Pentaquark state (u,d,s)=(100,100,100)MeV (u,d,s)=(100,100,240)MeV Mass (GeV)  Small L Large L   Small L Large L  1fm 2.4fm 4fm (u,d,s)=(240,240,100)MeV (u,d,s)=(240,240,240)MeV  Small L Large L   Small L Large L 

  16. NK scattering state vs Pentaquark state 1st excited state in (I,J,P)=(0,1/2,-) channel We find volume dependences.  NK scattering state???? Lattice is finite box If it is the scattering state with the relative momentum p=2π/L, we can estimate the energy as Here, we assume the absence of the interaction and that nucleon and kaon are point-particles.

  17. For example, this was applied to ….. I = 2 PI PI SCATTERING PHASE SHIFT WITH TWO FLAVORS OF O(A) IMPROVED DYNAMICAL QUARKS.By CP-PACS Collaboration (T. Yamazaki et al.) hep-lat/0402025 NK scattering state vs Pentaquark state We incorporate the interaction between N and K. M.Lusher Nucl.Phys.B354(1991)531 Outer wave func. Inner wave func. ordinary scattering wave Periodic Solution of Helmholtz Eq. The Eigenstate in the finite-volume lattice should be connected smoothly. However, we obtain almost same behavior as 2π/L  The weakness of NK interaction in this channel

  18. NK scattering state vs Pentaquark state (u,d,s)=(100,100,100)MeV (u,d,s)=(100,100,240)MeV MN+MK Mass (GeV) NK scattering  Small L Large L   Small L Large L  1fm 2.4fm 4fm (u,d,s)=(240,240,100)MeV (u,d,s)=(240,240,240)MeV  Small L Large L   Small L Large L 

  19. Large volume dependence Small Volume dependence NK scattering state vs Pentaquark state Spatial volume (1.6fm)3～(3.2fm)3 Current quark mass 100 MeV～240MeV The volume dependence of the 1st excited-state seem to be rather different from that of NK scattering. Current quark mass light Current quark mass heavy Above the theoretical curve Below the theoretical curve Existence of possible resonance states?

  20. NK scattering state vs Pentaquark state (u,d,s)=(100,100,100)MeV (u,d,s)=(100,100,240)MeV MN+MK Mass (GeV) NK scattering  Small L Large L   Small L Large L  1fm 2.4fm 4fm (u,d,s)=(240,240,100)MeV (u,d,s)=(240,240,240)MeV  Small L Large L   Small L Large L 

  21. Summary We have studied the ground-state and the 1st excited-state in (I, JP)=(0, 1/2－) channel using lattice QCD. We prepared two operators and constructed 2x2 correlation matrices and diagonalized them. As a result, we have successfully obtained the ground-state and 1st excited-state energies. Ground-state  NK scattering state with the relative momentum p=0 1st excited-state  rather different from the NK scattering state This might suggests the possibility of resonance states.

  22. Summary At least we can say…. If the 1st excited-state is Θ+(1540), it is broad object and it’s safe to use larger lattice than (2.5fm)3. The 1st excited-state seems to be rather different from NK scattering state. If it were NK scattering state, (the case Θ+(1540) does not exist……..?) Our result shows the volume dependence of the scattering state is nontrivial, which implies that we need careful treatment of the scattering state, for example, in the study of the phase shift using lattice QCD. Further study Full QCD calculations Improvement of quark action Large β(finer lattice) Higher statistics Detailed study of the quark mass dependence Analysis of the wave function …..

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