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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 ... first discovery of a manifestly exotic baryon by LEPS group at SPring-8, ... – PowerPoint PPT presentation

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Title: Pentaquark in Anisotropic Lattice QCD A possibility of a new 5Q resonance around 2'1 GeV


1
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) F. Okiharu (Nihon Univ.,
Japan)H. Suganuma (TITECH, Japan)
  • Plan of the talk
  • Introduction
  • General Formalism
  • Numerical Result on JP1/2()
  • A Further Investigation of the Negative parity
    state
  • New method with Hybrid Boundary Condition(HBC)
  • Numerical Result II
  • First Lattice QCD result on JP3/2(-)--- A
    possibility of a new 5Q resonance around m2.1
    GeV.
  • Summary/Discussion

preliminary
2
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 T(1540) is one of the most
    important topics.
  • Experimental determination of the parity of
    T(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,

3
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 JP3/2(-) channel.
preliminary
4
2.General Formalism (Part I JP1/2())
Interpolating field for T
As adopted in(1) J.Sugiyama et al.,
PLB581,167(2004).(2) S.Sasaki, PRL93,152001
(2004).
A non-NK type operator (I0, J1/2)
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
5
3. Numerical Result I
  • Lattice Parameter Setup
  • Gauge Config by standard Wilson gauge action
  • Lattice size 12396 (2.2fm)34.4fm in
    physical unit
  • ß 5.75
  • Lattice spacing from
    Sommer parameter r0.
  • Anisotropic latticeRenormalized anisotropy
    as/at4for 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
6
Negative parity channel (JP1/2(-))
Correlator
Effective mass
Single-state saturation is achieved.
Higher spectral contribution is gradually reduced.
best fit in the plateau
Plateau
Effective Mass
negligible !
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
7
Positive parity channel JP1/2()
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.
8
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, m1.75 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)

9
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
Hybrid Boundary Condition(HBC)
L
L
Cosequence on hadrons
Expected consequences on the spectra
Hybrid BC
Standar 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 detecting existence of compact 5Q
resonance in the region as
10
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 !
11
Numerical result II
Hybrid BC
Standard 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 parameter leads to mN1.74
    GeV, mK0.79 GeV
  • Expected shift of the NK threshold for L2.15 fm
    is

12
Combining the results from the other quark masses
  • data points The best fit value on the
    plateau.
  • solid lines NK(s-wave) threshold

We have not found a compact 5Q resonance in
JP1/2(-) in our calculation.
13
Part II First lattice QCD result on JP3/2(-)
channel
  • Spin of T is also not yet determined
    experimentally.
  • JP3/2(-) 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
    state The 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
    JP3/2 penta-quark yet.

14
Interpolating field (JP3/2(-))
NK-type interpolating field (I0,
Rarita-Schwinger formalism)
15
effective mass plot (JP3/2(-))
The best-fit mass is located above the NK
threshold and NK threshold !
16
Standard BC v.s. Hybrid BC (JP3/2(-))
Hybrid BC
StandardBC
70 MeV
plateau
plateau
NK(s-wave)
200MeV up
best-fit
best-fit
40MeV up
NK(s-wave)
NK(d-wave)
70MeV down
NK(d-wave)
preliminary
  • 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.

17
Chiral extrapolation (JP3/2(-))
Physical region m5Q 2.14(5) GeV
preliminary
NK threshold (s-wave)
JP3/2(-)
  • m5Q 2.14(5) GeV would be too massive to be
    identified as T(1540).
  • This may be a new compact 5Q resonance around 2.1
    GeV.(JP3/2(-), I0, S1)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.

18
6. Summary/discussion
  • We have studied T(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
  • JP1/2()
  • Non-NK type interpolating field
  • Positive parity m5Q 2.25(11) GeV --- too
    massive to be identified as T(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.
  • JP3/2(-) 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 T(1540).A
    possibility of a new 5Q resonance. (JP3/2(-),
    I0, S1)
  • Following possibilies would be interesting for
    T(1540)(a) small quark mass effects (and/or
    more elaborate chiral extrapolation), (b) large
    spatial volume, (c) dynamical quark(including
    pKN hepta-quark picture), (d) elaborate
    interpolating fields to fit the diquark picture.

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