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Anisotropic Lattice QCD studies of penta-quark baryons. 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 (Kyoto Univ., Japan).

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anisotropic lattice qcd studies of penta quark baryons
Anisotropic Lattice QCD studies of penta-quark baryons

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 (Kyoto Univ., Japan)

  • Plan of the talk:
  • Introduction
  • General Formalism
  • Numerical Result on JP=1/2(±)
  • A Further Investigation of the Negative parity state
    • Hybrid Boundary Condition(HBC) method
    • Numerical Result II
  • Anisotropic Lattice QCD result on JP=3/2(±)
  • Summary/Discussion

START

1 introduction
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(?) …
lattice qcd studies of the penta quarks
Lattice QCD studies of the penta quarks

★ A number of lattice QCD studies of 5Q system has been increased recently.

However, these results are 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 JP=1/2(-) state using a new method with the Hybrid boundary condition(HBC).(3) to provide the anisotropic lattice QCD result on JP=3/2(±) channelwith a large number of gauge configurations as Nconf=1000.

2 general formalism part i j p 1 2
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.

T

T

3 numerical result i
3. Numerical Result I

time

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
Negative parity channel (JP=1/2(-))

Correlator

Effective mass

Single-state saturation is achieved.

Higher spectral contribution is gradually reduced.

best fit in the plateau

Plateau

Effective Mass:

negligible !

“average” mass at time-slice t

If

then

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
Positive parity channel JP=1/2(+)

Correlator

Effective mass

Higher spectral contribution is gradually reduced.

Plateau

best fit in the plateau

Single-state saturation is achieved.

L

L

L

NK threshold (p-wave)

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

chiral extrapolation
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 .To obtain a low-lying state, it should appear below the raised NK threshold.
  • 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
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

L

L

L

Hybrid Boundary Condition(HBC)

Cosequence on hadrons

expected consequence on the spectrum
Expected consequence on the spectrum

Periodic BC(PBC):

Hybrid BC(HBC):

NK scattering states

r

=

p

p

3

/

L

min

★ A similar situation as the p-wave case can be introduced in the s-wave case by using HBC.

★ HBC helps us to clarify whether there exists a compact 5Q resonance statein the region as

  • NK-threshold is raised up due to finite voluem effect(~200 MeV if L~2fm.)
  • Compact 5Q resonance state is expected to be less sensitive to the change of the boundary condition.

~200 MeV

S-wave

numerical result ii
Numerical result II

Periodic BC(PBC)

Hybrid BC(HBC)

NK threshold(s-wave)

NK threshold(s-wave)

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
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 numerical result on j p 3 2 channel
Part II Numerical 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., PRD71,074021(2005).)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.
rarita schwinger interpolating fields
Rarita-Schwinger interpolating fields

NK*-type

color-fused NK*-type

diquark-type

spin 3/2 projection matrix:

spin 1/2 contributions+higher spectral contributions

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.

T

T

j p 3 2 state effective mass plot
JP=3/2(-)state (effective mass plot)

This correlator is too noisy !

chiral extrapolation j p 3 2
Chiral extrapolation (JP=3/2(-))

Physical quark mass region

○(circle)from NK*-type correlator

□(box)from color-fused NK*-type correlator

★ Results from diquark-type correlator are not shown due to huge statistical error.

NK* scattering states

  • In the physical quark mass region
  • NK*-type:m5Q= 2.17(4) GeV
  • Color-fused NK*-type: m5Q= 2.11(4) GeV
  • No evidence for a low-lying 5Q state

To obtain a low-lying 5Q state, it should appear below the raised NK threshold(d-wave) at least in the light quark mass region.

chiral extrapolation j p 3 218
Chiral extrapolation (JP=3/2(+))

Physical quark mass region

○(circle)from NK*-type correlator

□(box)from color-fused NK*-typecorrelator

△(triangle) from diquark-type correlator

  • In the physical quark mass region,
  • NK*-type:m5Q= 2.64(7) GeV
  • Color-fused NK*-type: m5Q= 2.48(10) GeV
  • Diquark-type:m5Q=2.42(6) GeV
  • No evidence for a low-lying 5Q states.

NK* scattering states

6 summary discussion
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(d) large number of gauge configurations: Ncf=1000 (for JP=3/2(±) states)
  • JP=1/2(±)
    • Non-NK type interpolating field:
    • JP=1/2(+):m5Q = 2.25(11) GeV --- too massive to be identified as Θ+(1540)
    • JP=1/2(-):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(±) [A large statistics as Ncf=1000 has played an important role.]
    • Three-types of interpolating field(NK*-type, color-fused NK*-type, diquark-type)
    • Only massive states after the chiral extrapolation:JP=3/2(-): JP=3/2(+):
  • HBC analysis is performed.Compact 5Q resonances are not found in our calculation.
  • 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.
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