Anisotropic lattice QCD studies of pentaquark antidecuplet

1
Anisotropic lattice QCD studies of penta-quark
anti-decuplet

• N. Ishii, H. Iida, H. Suganuma, M. Oka (TITECH)
• and
• F. Okiharu (Nihon University)
• T. Doi (RIKEN BNL Research Center)
• Y. Nemoto (Nagoya University)
• plan of the talk
• Introduction
• Parity Projection
• Numerical Result I
• Futher study of the negative parity state with a
  NEW METHOD
• Numerical Result II
• Summary/Discussion

START
2
1.Introduction

• Since the discovery of the first manifestly
  exotic hadron by LEPS group at
  SPring-8, the structure of T has been and is
  being intensively studied. Among others, the
  parity of the T is the hot topic.
• Positive parity is supported by
• Soliton models, Jaffe-Wilczek diquark model,
• Negative parity is supported by
• Constituent quark model, QCD sum rules,
• Lattice study of T is performed by
• S.Sasaki, hep-lat/0310014.
• F. Csikor et al., JHEP11(03)070.
• N.Mathur et al., hep-ph/0406196.
• T.-W. Chiu et al., hep-ph/0403020.
• MIT group.
• Still there are a number of unresolved issues.
• In this talk, our aim is to provide an accurate
  study of T by using the anisotropic lattice QCD.
  We will also perform a further analysis of the
  negative parity state by proposing a NEW METHOD.

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2.Parity Projection
scalar (0) diquark
pseudo-scalar (0-) diquark
Interpolating operator for iso-scalar T
Non-NK type operator This operator cannot
decompose into the product of N and K in the
nonrelativistic limit ? weak coupling to NK
continuum is expected !

• as adopted in
• J. Sugiyama et al., PLB581, 167 (2004)
• S. Sasaki, hep-lat/0310014

Depending on the boundary condition in time
The temporal correlator
Positive parity states dominate.
Negative parity states dominate.
T
T
Positive parity contribution cannot be negligible.
Negative parity contribution cannot be negligible.
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3. Numerical Result I

• Lattice Parameter Setup
• Gauge Config by standard Wilson plaquette 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 Fermion (clover) action.
• The extended operator with r0.4 fm (gaussian
  smearing) is adopted to suppress the higher
  spectral contributions. In this talk, we will
  consider the smear-point correlators (smeared
  source, point sink).

time
space
Finer lattice spacing in temporal directionfor
accureate measurement
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T (parity), smeared source point sink
Best Fit
Monotonical decrease
plateau single-state saturation is achieved.
Due to the limited extension in the temporal
direction
Excited-state contamination is gradually reduced.
Effective Mass
negligible !
NK threashold (p-wave) By neglecting the
interaction between N and K, NK threshold is
given as With the non-vanishing pmin due to the
finite box
If then Existence of the plateau
indicates the single-state saturation of the
correlator G(t).
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T(parity?), smeared source point sink
Monotonical decrease
Best Fit
plateau single-state saturation is achieved
Due to the limited extension in the temporal
direction
Excited-state contamination is gradually reduced.
NK threashold (s-wave) By neglecting the
interaction between N and K, NK threshold is
given as
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Chiral extrapolation
positive parity case
NK p-wave threshold
negative parity case

• Physical point
• Positive parity 2.24(11) GeV
• Negative parity 1.75(3) GeV

NK s-wave threshold

• Our data does not support the low-lying positive
  parity T.
• For negative parity case, m1.75 GeV is rather
  close to the empirical value 1.54 GeV. However,
  it should be confirmed that the observed state is
  actually a locarized resonance.(We will perform
  a further study in this direction from the next
  slide)

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4. Further study of the negative parity state
with a New Method
Due to the finiteness of the box, allowed spatial
momenta are quantized as 1. periodic BC 2.
anti-periodic BC
The spatial BOX
L
Hybrid Boundary Condition
L
L
Ordinary BC (u,d,s periodic BC)
Hybrid BC

• Expected Effects on the Spectrum
• NK threshold is shifted above due to the finite
  volume effect
• Localized resonance state is expected to be
  insensitive to the change of boundary condition.
  (an example)

NK scattering states
Hybrid BC can be used to detect the existence of
T as a localized resonance state in the interval
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An example(Response of the localized resonance
states to the change of boundary condition)
An established localized resonance state
Ordinary BC
Hybrid BC
Localized resonance states are insensitive to the
change of boundary condition.
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5. Numerical Result II
Ordinary BC
Hybrid BC
Best fit
Best fit
Threshold
Threshold
With our particular ?, mN 1.74 GeV mK
0.90 GeV The threshold is shifted above
as where
The plateau is shifted above by about 0.2GeV (
the shift of NK threshold).
? Localized resonance state does not exist in the
interval
? In particular, the observed plateau is a NK
scattering state.
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6. Summary/Discussion

• We have studied the penta quark T by using
  anisotropic lattice QCD. We used 504 gauge
  configurations (lattice size 12396) generated by
  the standard plaquette action at ß5.75 with the
  renormalized lattice anisotropy ?as/at4. O(a)
  improved Fermionic action (clover) is adopted
  ?0.1240, 0.1230, 0.1220, 0.1210.
• We adopted non-NK type operator
• We have adopted gaussian smearing of the size r
  0.4 fm to reduce the heigher spectral
  contributions in the correlator.
• In both parity cases, we found a stable plateau
  in the effective mass plot.Best-fit value after
  chiral extraporation potitive parity case
  2.24(11) GeV negative parity case 1.75(4) GeV
• Our data does not support the low-lying positive
  parity T.
• We have performed a further analysis in the
  negative parity case in order to confirm that the
  observed state is a localized resonance . For
  this purpose, we have proposed a NEW METHOD of
  Hybrid Boundary Condition. As a result, the
  plateau is shifted above by the expected amount
  (200 MeV), which suggests that the observed
  state in the negative parity case is a NK
  scattering state.(The smearing had played an
  important role.)
• For refinement, it is desirable to check the
  followings(i) small quark mass, (ii) more gauge
  configurations, (iii) spatial volume dependence,
  (iv) finer lattice spacings, (v) dynamical quark
  effects, (vi) MEM analysis of the correlators,
  etc.