Pentaquark in anisotropic lattice qcd a possibility of a new 5q resonance around 2 1 gev
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Pentaquark in Anisotropic Lattice QCD --- A possibility of a new 5Q resonance around 2.1 GeV N. Ishii (TITECH, Japan) T. Doi (RIKEN BNL) H. Iida (TITECH, Japan) Y. Nemoto (Nagoya Univ.) M. Oka (TITECH, Japan)

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Pentaquark in anisotropic lattice qcd a possibility of a new 5q resonance around 2 1 gev l.jpg
Pentaquark inAnisotropic Lattice QCD--- A possibility of a new 5Q resonance around 2.1 GeV

N. Ishii (TITECH, Japan)

T. Doi (RIKEN BNL)H. Iida (TITECH, Japan)Y. Nemoto (Nagoya Univ.)

M. Oka (TITECH, Japan)

F. Okiharu (Nihon Univ., Japan)H. Suganuma (TITECH, Japan)

  • Plan of the talk:

  • Introduction

  • General Formalism

  • Numerical Result on JP=1/2(±)

  • A Further Investigation of the Negative parity state

    • New method with Hybrid Boundary Condition(HBC)

    • Numerical Result II

  • First Lattice QCD result on JP=3/2(-)--- A possibility of a new 5Q resonance around m=2.1 GeV.

  • Summary/Discussion


1 introduction l.jpg
1. Introduction

Since the first discovery of a manifestly exotic baryon by LEPS group at SPring-8, enormous efforts have been devoted to the studies of penta quarks.

  • ★ The parity of Θ+(1540) is one of the most important topics.

  • Experimental determination of the parity of Θ+(1540) is difficult.

  • Theoretical opinions are divided into two pieces.

    • Positive parity is supported bySoliton models, Jaffe-Wilczek diquark model, ...

    • Negative parity is supported byNaive quark models, QCD sum rule, …

Lattice qcd studies of the penta quarks l.jpg
Lattice QCD studies of the penta quarks

There are a number of lattice QCD studies of penta quarks.

(1) F.Scikor et al., JHEP11(2003)070.(2) S.Sasaki, PRL93 (2004) 152001.(3) T.-W.Chiu et al., hep-ph/0403020.(4) N.Mathur et al., PRD70(2004)0745008.(5) N.Ishii et al., PRD71(2005) 034001.(6) C.Alexandrou et al., hep-lat/0409065; hep-lat/0503013.(7) T.T.Takahashi et al., hep-lat/0410025; hep-lat/0503019.(8) D.Sigaev et al., MIT group.(9) B.G.Lasscock et al., hep-lat/0503008.(10) F.Scikor et al., hep-lat/0503012.

However, these studies have not reached the consensus yet.

The aim of this talk is

(1) to provide a accurate data using anisotropic lattice QCD.(2) to provide a further studies of negative parity state using a new method with the Hybrid boundary condition(HBC).(3) to provide the 1st lattice QCD result on JP=3/2(-) channel.


2 general formalism part i j p 1 2 l.jpg
2.General Formalism (Part I: JP=1/2(±))

Interpolating field for Θ+

As adopted in(1) J.Sugiyama et al., PLB581,167(2004).(2) S.Sasaki, PRL93,152001 (2004).

A non-NK type operator: (I=0, J=1/2)

To reduce the overlap with NK scattering states

Temporal correlator

(“lower component”)

(“upper component”)

Positive parity states dominate.

Negative parity states dominate.

Positive parity contribution cannot become negligible.

Negative parity contribution cannot become negligible.



3 numerical result i l.jpg
3. Numerical Result I


2.2 fm

Finer lattice spacing along the temporal direction

  • Lattice Parameter Setup:

  • Gauge Config by standard Wilson gaugeaction:

    • Lattice size : 123×96[(2.2fm)3×4.4fm in physical unit]

    • β= 5.75

    • Lattice spacing: from Sommer parameter r0.

    • Anisotropic latticeRenormalized anisotropy: as/at=4for accurate measurements of correlators and masses

    • #(gauge config) = 504

    • The gauge configurations are separated by 500 pseudo heat-bath sweeps, after skipping 10000 thermalization sweeps.

  • O(a) improved Wilson quark (clover) action.

  • Smeared source to reduce higher spectral contributions

These values covers

Negative parity channel j p 1 2 l.jpg
Negative parity channel (JP=1/2(-))


Effective mass

Single-state saturation is achieved.

Higher spectral contribution is gradually reduced.

best fit in the plateau


Effective Mass:

negligible !



Existence of the plateau indicates the single-state saturation of the correlator G(t).

NK threshold(s-wave)By neglecting the interaction between N and K:

Positive parity channel j p 1 2 l.jpg
Positive parity channel JP=1/2(+)


Effective mass

Higher spectral contribution is gradually reduced.


best fit in the plateau

Single-state saturation is achieved.




NK threshold (p-wave)

The quantized spatial momenta are due to the finiteness of the box.

Chiral extrapolation l.jpg
Chiral extrapolation

NK threshold (p-wave)

At physical point

(1) Positive parity: 2.25(11) GeV(2) Negative parity: 1.75(3) GeV

NK threshold (s-wave)

  • Our data does not support the low-lying positive parity .

  • For negative parity channel, m=1.75 GeV is rather close to the empirical value 1.54 GeV. However, it should be clarified whether this state is a compact 5Q resonance or not.(We will perform a further study in this direction from the next slide)

4 further study of the negative parity state a new method with hybrid bc hbc l.jpg
4. Further study of the negative parity state.(a) NEW METHOD with Hybrid BC(HBC)

Spatial momentum is quantized due to finite volume effect:

1. periodic BC:

2. anti-periodic BC:

The spatial BOX


Hybrid Boundary Condition(HBC)



Cosequence on hadrons

Expected consequences on the spectra

Standar BC:

Hybrid BC:

  • NK threshold is raised due to finite volume effect.

  • Compact 5Q resonance states are expected to be less sensitive to the change of boundary condition.

NK scattering states

HBC helps us detectingexistence of compact 5Q resonance in the region as:

An example l.jpg
An example

Response of a compact resonance state to the change of boundary condition.

For this purpose, nucleon is not appropriate, because nucleon is sujbect to the anti-periodic BC.

A localized resonance is less sensitive to the change of boundary condition !

Numerical result ii l.jpg
Numerical result II

Standard BC

Hybrid BC

The plateau is shifted above by the expected amount.

(1) No compact 5Q resonance exists in the region as

(2) The state observed in the negative parity channel turns out to be an NK scattering state.

  • The hopping parameterleads to mN=1.74GeV, mK=0.79 GeV

  • Expected shift of the NK threshold for L=2.15 fm is

Combining the results from the other quark masses l.jpg
Combining the results from the other quark masses

  • data pointsThe best fit value on the plateau.

  • solid linesNK(s-wave) threshold

We have not found a compact 5Q resonance in JP=1/2(-) in our calculation.

Part ii first lattice qcd result on j p 3 2 channel l.jpg
Part II First lattice QCD result on JP=3/2(-) channel

  • Spin of Θ+ is also not yet determined experimentally.

  • JP=3/2(-) possibility can solve the puzzle of the narrow decay width.(proposed by A.Hosaka et al., hep-ph/0409102.)Advantage:(a) It allows the configuration of (0s)5.(b) It decays into a d-wave KN state.Suppressed overlap to d-wave KN stateThe decay width is expected to be significantly narrow.Disadvantage:(a) The color-magnetic interaction makes it massive.If some contribution can cancel the color-magnetic interaction to make its mass around 1540, we will obtain a penta-quark with a significantly narrow width.

  • There have been no lattice QCD calculations for JP=3/2 penta-quark yet.

Interpolating field j p 3 2 l.jpg
Interpolating field (JP=3/2(-))

spin 1/2 contributions+higher spectral contributions

spin 3/2 projection matrix:

Temporal correlator

(“lower component”)

(“upper component”)

Negative parity states dominate.

Positive parity states dominate.

Negative parity contribution cannot become negligible.

Positive parity contribution cannot become negligible.



NK*-type interpolating field (I=0, Rarita-Schwinger formalism)

Effective mass plot j p 3 2 l.jpg
effective mass plot (JP=3/2(-))

NK* threshold (s-wave):

NK threshold (d-wave):

Excited state’s contribution is gradually reduced.

Single-state saturation is expected to be achieved.



Best-fit mass in the plateau:



The best-fit mass is located above the NK* threshold and NK threshold !

Standard bc v s hybrid bc j p 3 2 l.jpg
Standard BC v.s. Hybrid BC (JP=3/2(-))


This state may be a compact resonance state.

Hybrid BC

70 MeV





200MeV up



40MeV up



70MeV down



  • After twisting the boundary condition to HBC:

  • The location of the best fit mass is almost unchanged.

  • It appears below NK* threshold by 70 MeV.

Chiral extrapolation j p 3 2 l.jpg
Chiral extrapolation (JP=3/2(-))

Physical region:

m5Q = 2.14(5) GeV


NK* threshold (s-wave)


  • m5Q = 2.14(5) GeV would be too massive to be identified as Θ+(1540).

  • This may be a new compact 5Q resonance around 2.1 GeV.(JP=3/2(-), I=0, S=+1)Several comments on this state:(1) Quenched QCD results should be understood to contain about ±10% error.(The mass is better understood to be located in the region 1.9 GeV – 2.3 GeV.)(2) The decay width could be less narrow. --- The state appears above NK* threshold. --- Quenched QCD tends to underestimate the decay width. (K* does not decay)(3) Still, it would be interesting to investigate this state into detail.

6 summary discussion l.jpg
6. Summary/discussion

  • We have studied Θ+(1540) by using the anisotropic lattice QCD. For acuracy,(a) renormalized anisotropy as /at = 4(b) O(a) improved Wilson (clover) action for quarks(c) smeared source

  • JP=1/2(±)

    • Non-NK type interpolating field:

    • Positive parity:m5Q = 2.25(11) GeV --- too massive to be identified as Θ+(1540)

    • Negative parity:m5Q = 1.75(4) GeV --- rather close to the observed value.

    • We have proposed a new method (Hybrid BC [HBC]).HBC analysis showsthe state(1.75 GeV) is not a compact 5Q state but an NK scattering state.

  • JP=3/2(-) [1st lattice QCD result]

    • NK*-type interpolating field:

    • HBC analysis indicatesthere is a state, which may be a compact 5Q resonance.

    • Chiral extrapolation leads to m5Q = 2.14(5) GeV--- too massive to be identified as Θ+(1540).A possibility of a new 5Q resonance. (JP=3/2(-), I=0, S=+1)

  • Following possibilies would be interesting for Θ+(1540):(a) small quark mass effects (and/or more elaborate chiral extrapolation), (b) large spatial volume, (c) dynamical quark(including πKN hepta-quark picture), (d) elaborate interpolating fields to fit the diquark picture.


Analysis of the other operators are currently going on. (Operator dependences are seen in our results)