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

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 pp.          Published in Phys.Rev.D68:054502,2003             e-Print Archive: hep-lat/

4

5 T. Burch , C. Gattringer, L. Ya. Glozman, C. Hagen, D. Hierl, C. B
T. Burch , C. Gattringer, L. Ya. Glozman, C. Hagen, D. Hierl, C.B. Lang, A. Schafer Published in Phys.Rev.D74:014504, e-Print Archive: hep-lat/ 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: ,2005. D. Guadagnoli et al. Phys.Lett.B604:74-81,2004.

6 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 T.Nakano etal. Phys.Rev.Lett.91(2003)012002

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

8 何故このような事に?

9 We suffer from the contaminations of the other scattering 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 Euclidean time evolution by exp(-Ht) Creation at t=0 Annihilation at t=T Energy of the ground state

10 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.

11 Spectral weight How to distinguish??
~ 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

12 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 3x3 or more is needed Too small for hadrons Before the final quantitative conclusions.. Need to take a continuum and chiral-limit properly in unquenched calculations.

13 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] gauge configurations 103 x 24 [(2.0 fm)3 x 4.8fm] gauge configurations 123 x 24 [(2.4 fm)3 x 4.8fm] gauge configurations 163 x 24 [(3.2 fm)3 x 4.8fm] 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

14 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

15 Quality (I, JP) = (0, 1/2—)

16 It is expected to be the scattering state of Nucleon and Kaon,
The lowest state in (I, JP)=(0, 1/2-) channel (u,d,s)=(100,100,240)MeV (u,d,s)=(240,240,240)MeV Mass (GeV) 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. MN+MK  Small L Large L   Small L Large L  1fm fm fm (u,d,s)=(100,100,100)MeV (u,d,s)=(240,240,100)MeV  Small L Large L   Small L Large L 

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

18 Spectral weight How to distinguish??
~ 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

19 (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

20 Fermionic Determinant
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。 Fermionic Determinant Det W Quark model 的?

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

22 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 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

23 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。
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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