Anisotropic lattice QCD studies of pentaquarks and tetraquarks

1
Anisotropic lattice QCD studies of penta-quarks
and tetra-quarks
N. Ishii (Univ. of Tokyo) in
collaboration with T. Doi (Riken
BNL)H. Iida (TITECH)Y. Nemoto
(Nagoya Univ.)M. Oka (TITECH)F.
Okiharu (Nihon Univ.)H. Suganuma
(Kyoto Univ.)K. Tsumura (Kyoto Univ.)
Plan of the talk1 Introduction2 General
Formalisms3 Numerical Results4
Summary/Discussion(5 Tetra-quarks(4Q)) See
Phys.Rev.D71,034001(2005) D72,074503(2005) for
detail.
START
2
1.Introduction

• One of the most important issues for T(1540) is
  to understand
• its extremely narrow decay width
  Glt1 MeV.
• Several ideas have been proposed as
• I2 assignment
• Jaffe-Wilczeks diquark picture ? JP1/2()
  and 3/2()
• pKN hepta-quark picture ?
  JP1/2()
• The string picture
• JP3/2(-) assignment ?
  JP3/2(-)

• In this talk, we are mainly interested in
  JP3/2() possibilities
• We first present our numerical results on
  JP1/2() penta-quarks brieflyemplyoing a
  diquak-type interpolating fieldusing a flavor
  dependent boundary condition(HBC)
• We then present our numerical results on
  JP3/2() penta-quarksemploying three
  Rarita-Schwinger interpolating fieldsusing 1000
  gauge field configurations for high statistics

3
JP3/2() possibilities

• Spin of T has not yet been determined
  experimentally.
• JP3/2(-) assignment 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 only decays
  into a d-wave KN state.Suppressed overlap
  between these two states The decay
  width is expected to be significantly
  narrow.Disadvantage(a) The constatituent
  quark picture suggests such a 5Q state is quite
  heavy. (? due to the color-magnetic
  interaction)Since it is not apriori clear
  whether such a conventional framework can be
  applied to a new exotic 5Q system as T(1540) or
  not, it is desirable to perform a direct lattice
  QCD calculation.
• JP3/2() is also interesting, which is suggested
  by the diquark picture.

HOWEVER
The total spin(parity) is 1/2() or 3/2().?
3/2() penta-quark may have a narrow decay width !
p-wave
4
Lattice QCD studies of the penta quarks
? There are several lattice QCD calculations of
penta-quarks available. (published one
only)
SPIN 1/2
SPIN 3/2
Most of them are devoted to spin 1/2 states
except for the recent two.
5
2.General Formalism

• Lattice QCD 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 for JP1/2()
  1000 for JP3/2()
• O(a) improved Wilson quark (clover) action.The
  quark mass covers the region ms lt mq lt 2 m s
• Smeared source to reduce higher spectral
  contributions

6
The interpolating fields
We consider the following iso-scalar
interpolating fields
? A diquark-type interplating fields for
JP1/2() states
(scalar)
(pseudo scalar)
? Three Rarita-Schwinger interplating fields for
JP3/2() states
NK-type
color-twisted NK-type
diquark-type
(scalar)
(vector)
7
Hybrid Boundary Condition(HBC)
We utilize a flavor dependent spatial BC (Hybrid
BC (HBC)). (We use HBC in addition
to the standard periodic BC(PBC))
Hybrid Boundary Condition(HBC)
Cosequence on hadrons
? NK and NK threshold energies(s-wave) are
raised due to , ? T,if it is a
compact resonance, will not be affected so
much. HBC can be used to determine whether a
state is a compact resonance or not. ? In the
case of p/d wave, HBC serves as another boundary
condition(other than PBC).
With HBC
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3.Numerical Results JP1/2() states (effective
mass plots)
Effective mass is defined as which can be
considered as an weighted average of massesat
each time-slice t.
Excited state contributions are reducing
A single state dominate the correlator G(t) in
this region.

• JP1/2(-) stateA state appears slightly above
  the NK threshold (mNmK).
• JP1/2() stateA state appears above the
  raised NK threshold (due to the finite box).?
  rather massive !

9
Effective mass plot
The correlator can be expressed as a sum
The Effective Mass is defined as
This can be considered as average of masses at
each time-slice t
If G(t) is dominated by a single state
negligible !
Then we have,
(Constant effective mass)
A plateau in the effective mass plot
indicatesG(t) is saturated by a single-state
contribution.
10
Chiral extrapolation (JP1/2())
NK threshold (p-wave)
At physical point (1) JP1/2() 2.24(11)
GeV(2) JP1/2(-) 1.75(3) GeV
NK threshold (s-wave)

• Our data does not support a low-lying JP1/2()
  penta-quark.
• For JP1/2(-) state, the mass(1.75 GeV) is OK
  !Still, it is necessary to check whether it is
  not an NK scattering state but a compact
  resonance.? HBC analysis

11
HBC analysis (JP1/2(-) state)
PBC
HBC

• NK(s-wave) threshold is raised up by 210 MeV.
• The best fit mass m5Q is raised up by a similar
  amount.
• ? No compact 5Q resonance exists in the region
• ? The state observed in JP1/2(-) is an NK
  scattering state.

12
Combining the results from all the other hopping
parameters.

• data points The best fit value over the
  plateau.
• solid lines NK(s-wave) threshold

The states observed in are NK
scattering states !
13
Numerical Results JP3/2(-) state (effective
mass plot)
plateau
twisted
plateau

The plateaus appearabove the NK-threshold and
above the raised NK threshold.
This correlator is too noisy !Fit is not
performed.
14
NK(JP3/2(-))

• NK(s-wave) threshold is raised up by 179 MeV.
• NK(d-wave) threshold is lowered down by 66
  MeV.
• Best-fit(m5Q) is raised up by 80 MeV.Its value
  is almost consistent with NK-threshold(s-wave).
  This state is an NK scattering state.A large
  number of config. Nconf1000 has played a
  crucial role.

15
color-twisted NK(JP3/2(-))
twisted
twisted

• The situation is similar to the NK-correlator.
• NK(s-wave) threshold is raised up by 179 MeV.
• NK(d-wave) threshold is lowered down by 66
  MeV.
• Best-fit(m5Q) is raised up by 90 MeV.Its value
  is almost consistent with the NK-threshold.
• This state is also an NK scattering
  state.

16
Chiral extrapolation (JP3/2(-))
Physical quark mass region
?(circle) from NK-type correlator ?(box)
from color-twisted NK-type correlator
Due to the limited time, we cannot show HBC
analysis.
HBC analysis suggeststhese states are
NK(s-wave) scattering states

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

17
JP3/2() state (effective mass plot)
twisted
plateau
plateau
The plateaus appearabove the raised
NK-threshold and above the raised NK threshold.
plateau
18
NK(JP3/2())

• Changes in the two-particle spectrum are too
  small in JP3/2() channel.
• NK(s-wave) threshold is raised up by 170 MeV.
• NK(p-wave) threshold is lowered down by 57
  MeV.
• NK(p-wave) threshold is lowered down by 66
  MeV.
• Best-fit(m5Q) is raised up by 60 MeV.Its value
  coincides with NK(s-wave) threshold.
• This state is a NK(s-wave) threshold.

19
Color-twisted NK(JP3/2())
twisted
twisted

• Changes in two-particle spectrum are too small in
  JP3/2() channel.
• NK(p-wave) threshold is lowered down by 57
  MeV.
• NK(p-wave) threshold is lowered down by 66
  MeV.
• Best-fit(m5Q) is raised up by 90 MeV.
• This state is an NK scattering state.

20
Diquark-type(JP3/2())

• Changes in the two-particle spectrum are too
  small in JP3/2() channel.
• NK(p-wave) threshold is lowered down by 57
  MeV.
• NK(p-wave) threshold is lowered down by 66
  MeV.
• Best-fit(m5Q) is raised up by 80 MeV.
• This state is an NK-scattering state.

21
Chiral extrapolation (JP3/2())
Physical quark mass region
?(circle) from NK-type correlator ?(box)
from color-twisted NK-type
correlator ?(triangle) from diquark-type
correlator
Due to the limited time, we cannot show HBC
analysis.
HBC analysis suggests
NK(s-wave) scattering state

• In the physical quark mass region,
• NK-type m5Q 2.64(7)
  GeV
• Color-twisted NK-type m5Q 2.48(10) GeV
• Diquark-type m5Q2.42(6) GeV
• No evidence for a low-lying 5Q states.

NK(p-wave) scattering states
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4. Summary/discussion

• We have studied spin1/2 and 3/2 penta-quarks 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 Ncf1000 for JP3/2()
• JP1/2() with a diquark-type interpolating
  field
• JP1/2(-) state
  JP1/2() state
• HBC analysis shows that this state is an NK
  scattering state.
• JP3/2() A large statistics as Ncf1000 has
  played an important role.
• Three interpolating fields (NK-type,
  color-twisted NK-type, diquark-type)
• Only massive states after the chiral
  extrapolationJP3/2(-) state
  JP3/2() state
• HBC analysis suggests that these 5Q states are
  NK and NK scattering states.
• Following possibilies would be interesting for
  T(1540)
• Small quark mass effect(and/or elaborate chiral
  extrapolation)
• Large spatial volume
• Dynamical quarks
• Elaborate interpolating fields to fit the diquark
  picture
• pKN hepta-quark picture

Too heavy to be identified as T(1540)
See for detailPhys. Rev. D71,034001
(2005)Phys. Rev. D72,074503 (2005)
23
5.Tetra-quarks(4Q) (work in progress)
A lattice QCD calculation using the pKN
interpolating field(7-body op.) is difficult. pK
subsystem is much easier to study.It is a 4Q
system with the quantum number of ?. ? together
with f0(600), f0(980), a0(980) forms the scalar
nonet, which are candidates of tetra(4Q) quark
states.
pp scattering state
Since these tetra-quarks are interesting target
in their own right, we are currently performing
4Q lattice QCD calculations from a more general
point of view.
0 meson (chiral extrapolation)
pp threshold(HBC)
4Q with HBC
4Q with PBC
PRELIMINARY
Our preliminary result suggests an existence of a
4Q resonance. work in progress.
pp threshold(PBC)