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Lattice QCD study of exotic hadrons

Lattice QCD study of exotic hadrons. Toru T. Takahashi with Takashi Umeda, Tetsuya Onogi, Teiji Kunihiro. ---Yukawa Institute for Theoretical Physics---. ・格子 QCD を用いた、 Pentaquark の研究 ・ topics, 今後の可能性？. 許可を取っていないため、他グループのスライドをそのまま含む内容は、割愛させていただきます。. Quantum Chromodynamics.

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Lattice QCD study of exotic hadrons

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  1. Lattice QCD study of exotic hadrons Toru T. Takahashi with Takashi Umeda, Tetsuya Onogi, Teiji Kunihiro ---Yukawa Institute for Theoretical Physics--- ・格子QCDを用いた、Pentaquark の研究 ・topics, 今後の可能性？ 許可を取っていないため、他グループのスライドをそのまま含む内容は、割愛させていただきます。

  2. Quantum Chromodynamics Nuclear or Hadron Physics Quantum manybody system SU(3) gauge theory proton neutron …… Quarks (fund. rep.) Hadrons GAP!! (adjoint rep.) Mesons p, r, w,….. Gluons Strong coupling nature of QCD Lattice QCD calculation Analytic study is still difficult Introduction Want to understand the hadron dynamics in terms of QCD

  3. Lattice QCD calculations LIGHT HADRON SPECTROSCOPY WITH TWO FLAVORS OF O(A) IMPROVED DYNAMICAL QUARKS.By JLQCD Collaboration (S. Aoki et al.). KEK-CP-136, Dec 2002. 52pp. Published in Phys.Rev.D68:054502,2003e-Print Archive: hep-lat/0212039

  4. T. Burch , C. Gattringer, L. Ya. Glozman, C. Hagen, D. Hierl, C.B. Lang, A. Schafer Published in Phys.Rev.D74:014504,2006. e-Print Archive: hep-lat/0604019 実験値を再現できないということではなく、その再現はそれほどtrivialではないということです。 cf) N. Mathur et al. Phys.Lett.B605:137-143,2005. D. Guadagnoli et al. Phys.Lett.B604:74-81,2004.

  5. T.Nakano etal. Phys.Rev.Lett.91(2003)012002 基底状態のハドロンについては、それなりに高精度で解析されている しかし、 それ以外に関しては、まだ始まって間もない。と、言えるかもしれない。  いろいろな困難もその原因の一つ

  6. Csikor et al. (No pentaquark resonance) (No pentaquark resonance) Kentuchy Group (No pentaquark resonance) TITECH Group (No pentaquark resonance) Lasscock et al. (No pentaquark resonance) BGR collaboration (No pentaquark resonance in 1/2 positive) S.Sasaki (Pentaquark resonance in 1/2 negative) Alexandrou et al. Chiu & Hsieh (Pentaquark resonance in 1/2 positive) (Pentaquark resonance in 1/2 negative) YITP -- Lattice QCD study of the pentaquark resonance --

  7. 何故このような事に？

  8. Euclidean time evolution by exp(-Ht) Energy of the ground state 格子QCDでは何を測っているのか？ Difficulty in the lattice QCD calculation We suffer from the contaminations of the other scattering state. Correlation between operators Annihilation at t=T Creation at t=0

  9. 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.

  10. How to distinguish?? Spectral weight ～ overlaps of operators with each quantum state Proposed by Kentucky group normalization of each state normalization of quark fields ↓ Volume dep. of spectral weights volume of the system Resonance state  small volume dependeces

  11. Too small for hadrons 3x3 or more is needed Before the final quantitative conclusions.. Need to take a continuum and chiral-limit properly in unquenched calculations. Difficulties ・Not a lightest state in the channel we have to extract 2 states at lease →diagonalization of correlation matrices ・Contaminations by scattering states we have to distinguish it from scatt. states →volume dep. (energy or weight factors) ・ discretized lattice momenta in a finite box dilemma of spatial volume

  12. 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) (170MeV, 170MeV, 100MeV) (100MeV, 100MeV, 100MeV) Done on SX5 at RCNP,Osaka University and SR8000 at KEK

  13. Ground state and 1st excited state in I=0,J=1/2 channel Interpolating operators Nucleon Kaon N+K like operator Pentaquark like operator Spinor structure : same Color structure : different

  14. Quality (I, JP) = (0, 1/2—)

  15. 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. The lowest state in (I, JP)=(0, 1/2-) channel (u,d,s)=(240,240,240)MeV (u,d,s)=(100,100,240)MeV Mass (GeV) MN+MK  Small L Large L   Small L Large L  1fm 2.4fm 4fm (u,d,s)=(100,100,100)MeV (u,d,s)=(240,240,100)MeV  Small L Large L   Small L Large L 

  16. The 2nd-lowest state in (I, JP)=(0, 1/2-) channel (u,d,s)=(240,240,240)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)=(100,100,100)MeV (u,d,s)=(240,240,100)MeV  Small L Large L   Small L Large L 

  17. How to distinguish?? Spectral weight ～ overlaps of operators with each quantum state Proposed by Kentucky group normalization of each state normalization of quark fields ↓ Volume dep. of spectral weights volume of the system Resonance state  small volume dependeces

  18. (I, JP)=(0, 1/2-) Spectral weight NEGATIVE parity channel Ground-state Expected to be NK scattering with relative momentum p=0 1/V dependence 1st excited-state Expected to be resonance state no volumedependence

  19. Fermionic Determinant Det W YITP グループの主張： 為すべきことを、可能な範囲でやった結果、I=0, 1/2 – channel のthreshold の少し上に、pentaquark resonanceと 思われる状態を発見した。ただし、quench 近似。 クォークの真空偏極の効果を含まない。 Quark model 的？

  20. MIT Group, PoS LAT2005:069,2006 そう主張するのは、YITPグループだけではないのか？ Channel  I=0, spin=1/2 negative-parity

  21. 最大公約数的な結論？ ・quench近似の範囲内では、Θ+(1540)のように、thresholdのすぐ上 のresonanceは見つかっていない。  YITP Group, MIT Groupともに、少し重めに出る？ ・現在の解析で、resonanceのような状態を見たのは、 ほとんどが、I=0, spin=1/2, negative-parity channel  ただ一つ、positive-parity channelのresonanceを主張する グループがあるが、spectral weight等の解析をしていない。 Θ+(1540)そのものの有無については、確定的ではないが、 I=0, spin=1/2, negative parity channel、thresholdの少し上にresonanceの構造？  肥山さんの計算 uudds以外の、pentaquarkの可能性？ 我々の今の計算はs-quark程度の質量 依然としてinconsistency が残るように思える ・全ての計算がquench近似 ・全てのsystematic errorをコントロールしている結果が無い ・quark 質量も重め

  22. 現状では、基底状態以外のハドロンの格子QCD計算はまだ現状では、基底状態以外のハドロンの格子QCD計算はまだ 始まって間もないと言える。 少しの間、質量の正確な再現などに注力されると考える。 • これから？ • 崩壊幅など、ハドロン－ハドロン相互作用なども 解析の手が伸びていくと思われる。

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