InterQuark Potentials in Baryons and MultiQuark Systems in QCD

1
Inter-Quark Potentials in Baryons and
Multi-Quark Systems in QCD
H. Suganuma, A. Yamamoto, H. Iida, N. Sakumichi
(Kyoto Univ.) with T.T.Takahashi (Kyoto Univ.),
F. Okiharu (Nihon U.)
Contents 1. Three-Quark Potential in SU(3)
lattice QCD 2. Multi-Quark Potential in SU(3)
lattice QCD 3. Heavy-heavy-light quark potential
and Light-quark effects to the
inter-two-quark interaction in baryons
(SU(3) lattice QCD and Analytical model
calculation)
Chiral 07, Nov 13-16 2007, RCNP Osaka
2
Inter-quark potential in QCD

• In 1979, M.Creutz performed the first application
  of lattice QCD simulation for the quark-antiquark
  potential using the Wilson loop.
• Since then, the study of the inter-quark force
  has been one of the central issues in lattice
  QCD.
• Actually, in hadron physics, the inter-quark
  force can be regarded as an elementary quantity
  to connect the quark world to the hadron
  world, and plays an important role to hadron
  properties.
• In 1999, in addition to the quark-antiquark
  potential, we performed the first accurate
  reliable lattice QCD study for the three-quark
  (3Q) potential, which is responsible to the
  baryon structure at the quark-gluon level.
• Furthermore, in 2005, we performed the first
  lattice QCD study for the multi-quark potentials,
  i.e., 4Q and 5Q potentials, which give essential
  information for the multi-quark hadron physics.
• Note also that the study of 3Q and multi-quark
  potentials is directly related to the quark
  confinement properties in baryons and multi-quark
  hadrons.
• First, I review the lattice QCD results for
  static inter-quark potentials.

3
Quark-antiquark static potential in Lattice QCD
M.Creutz (1979,80)
quark
anti-quark
r
t
T
Wilson loop
The quark-antiquark potential can be obtained
from the Wilson Loop.
4
Quark-antiquark static potential in Lattice QCD
M.Creutz (1979,80) Summarized lattice QCD
data G.S.Bali (2001) Takahashi, H.S. et al.
(2002) JLQCD (2003)
quark
anti-quark
r00.5fmunit
r
t
T
Wilson loop
1 T
The quark-antiquark potential can be obtained
from the Wilson Loop.
V(r) -lim lnltWgtT
T?8
5
Quark-antiquark static potential in Lattice QCD
M.Creutz (1979,80) Summarized lattice QCD
data G.S.Bali (2001) Takahashi, H.S. et al.
(2002) JLQCD (2003)
quark
anti-quark
r00.5fmunit
g2 3p
1 r
V(r) - sr
The quark-antiquark potential V(r) is well
described by Coulomb Linear Potential. s?
0.89 GeV/fm
6
Quark-antiquark static potential in Lattice QCD
M.Creutz (1979,80) Summarized lattice QCD
data G.S.Bali (2001) Takahashi, H.S. et al.
(2002) JLQCD (2003)
quark
anti-quark
r00.5fmunit
g2 3p
1 r
V(r) - sr
quark
anti-quark
-
At the short distances, the Q-Q potential behaves
as the Coulomb-type potential, which is expected
from the one-gluon-exchange (OGE) process.
g
g
7
Quark-antiquark static potential in Lattice QCD
M.Creutz (1979,80) Summarized lattice QCD
data G.S.Bali (2001) Takahashi, H.S. et al.
(2002) JLQCD (2003)
quark
anti-quark
r00.5fmunit
At the long distances, the Q-Q potential behaves
as a linear arising potential like a
condenser, which indicates one-dimensional
squeezing of the color-electric flux between
quark and antiquark.
-
g2 3p
1 r
V(r) - sr
8
Quark-antiquark static potential in Lattice QCD
M.Creutz (1979,80) Summarized lattice QCD
data G.S.Bali (2001) Takahashi, H.S. et al.
(2002) JLQCD (2003)
quark
anti-quark
r00.5fmunit
r
t
g2 3p
1 r
V(r) - sr
T
Wilson loop
quark
anti-quark
-
One-dimensional squeezing of color flux between q
and q
g
g
anti-quark
quark
9
Baryonic Three-Quark Potential in Lattice QCD
quark
quark
What Shape of Color Flux? Confining Force?
quark
Before our study, there was almost No lattice
QCD study for the Three-Quark Potential. This is
not so trivial especially for quark confining
force in baryons at long distance.
10
PRThis is the cover of a recent textbook
written by Hosaka and Toki.
11
PRThis is the cover of a recent textbook
written by Hosaka and Toki.
This is a nice textbook for the introduction
to quark-hadron physics
12
PRThis is the cover of a recent textbook
written by Hosaka and Toki.
But!
Look! Is this a correct picture for the color
flux tube inside baryons ?
13
Systematical Studies for Three and Multi-Quark
Potentials in Lattice QCD

• Detailed Analysis of Tetraquark Potential and
  Flip Flop in SU(3) Lattice QCD F. Okiharu, H.
  Suganuma and T.T. Takahashi
• Physical Review D72 (2005) 014505 (17
  pages).
• First Study for the Pentaquark Potential in
  SU(3) Lattice QCD F. Okiharu, H. Suganuma and
  T.T. Takahashi
• Physical Review Letters 94 (2005) 192001 (4
  pages).
• Detailed Analysis of the Gluonic Excitation in
  the 3Q System in Lattice QCD T.T. Takahashi and
  H. Suganuma
• Physical Review D70 (2004) 074506 (13
  pages).
• Gluonic Excitation of the Three-Quark System in
  SU(3) Lattice QCDT.T. Takahashi and H. Suganuma
  
• Physical Review Letters 90 (2003) 182001 (4
  pages).
• Detailed Analysis of the Three Quark Potential
  in SU(3) Lattice QCD T.T. Takahashi, H.
  Suganuma et al.
• Physical Review D65 (2002) 114509 (19
  pages).
• Three-Quark Potential in SU(3) Lattice QCDT.T.
  Takahashi, H. Suganuma et al.
• Physical Review Letters 86 (2001) 18-21.

14
t
1 T
V3Q(r) -lim lnltW3QgtT
T?8
15
k
j
i
(i, j, k) characterize the shape of the 3Q
triangle.
16
k
j
i
(i, j, k) characterize the shape of the 3Q
triangle.
17
k
j
i
(i, j, k) characterize the shape of the 3Q
triangle.
18
k
j
i
(i, j, k) characterize the shape of the 3Q
triangle.
19
n
k
-m
l
(l, m, n) characterize the shape of another type
of 3Q triangles.
j
i
(i, j, k) characterize the shape of the 3Q
triangle.
More than 300 different shapes of 3Q triangles
are analyzed in total.
20
Lmin total length of string linking three
valence quarks
21
(No Transcript)
22
Baryonic Three-Quark Potential in Lattice QCD
Takahashi, H.S. et al. PRL 86 (2001)
18 Takahashi, H.S. et al. PRD65 (2002)114509
Takahashi, H.S. PRL 90 (2003) Takahashi, H.S.
PRD70 (2004) 074506 Okiharu, H.S. et al. PRD72
(2005) 014505
quark
quark
What Shape of Color Flux? Confining Force?
quark
Before our study, there was almost No lattice
QCD study for the Three-Quark Potential
23
Baryonic Three-Quark Potential in Lattice QCD
Takahashi, H.S. et al. PRL 86 (2001)
18 Takahashi, H.S. et al. PRD65 (2002)114509
Takahashi, H.S. PRL 90 (2003) Takahashi, H.S.
PRD70 (2004) 074506 Okiharu, H.S. et al. PRD72
(2005) 014505
conf
V3Q(r)
24
Baryonic Three-Quark Potential in Lattice QCD
Takahashi, H.S. et al. PRL 86 (2001)
18 Takahashi, H.S. et al. PRD65 (2002)114509
Takahashi, H.S. PRL 90 (2003) Takahashi, H.S.
PRD70 (2004) 074506 Okiharu, H.S. et al. PRD72
(2005) 014505
conf
V3Q(r)
quark
quark
color electric flux
quark
Lmin total length of string linking three
valence quarks
g2 4p
3
TiaTja ri - rj
V3Q(r) ? sLmin
iltj
One-Gluon-Exchange Coulomb potential
Linear potential based on string picture
25
Lattice QCD result for Color Flux-Tube Formation
in baryons
H. Ichie et al., Nucl. Phys. A721, 899 (2003)
26
The status of our studies of 3Q potential

• Our studies of the 3Q potential are introduced as
  one
• whole subsection with citing 4 our papers in 3rd
  edition
• of Lattice Gauge Theories, which is one of the
  most
• popular lattice QCD text books.

27
PRThis is the cover of a recent textbook
written by Hosaka and Toki.
?
28
PRThis is the cover of a recent textbook
written by Hosaka and Toki.
I have corrected it with the appropriate picture
for the color flux tube inside baryons.
29
PRThis is the cover of a recent textbook
written by Hosaka and Toki.
Without a matter of the cover, this is a nice
textbook for the introduction to quark-hadron
physics.
I have corrected it with the appropriate picture
for the color flux tube inside baryons.
30
PRThis is the cover of the proceedings of
Confinement Conference.
31
Multi-Quark Hadrons and Multi-Quark Potentials

• In these years, there have been reported
  experimental
• discoveries of several candidates of multi-quark
  hadrons
• such as T(1530), X(3872) and so on.
• Very recently, the discovery of a charged
  charmonium
• Z(4430) (ccud) is reported at KEK-Belle
  experiment.

-
-
32
Tetra-Quark Z(4430) from KEK press release
The charged charmonium Z(4430) is a manifest
Tetra-Quark hadron composed by ccud.
-
-
33
Multi-Quark Hadrons and Multi-Quark Potentials

• In these years, there have been reported
  experimental
• discoveries of several candidates of multi-quark
  hadrons
• such as T(1530), X(3872) and so on.
• Very recently, the discovery of a charged
  charmonium
• Z(4430) (ccud) is reported at KEK-Belle
  experiment.
• For the quark-model calculation of the
  multi-quark system,
• it is rather important to clarify the multi-quark
  potential, which
• gives the quark-model Hamiltonian for multi-quark
  system.
• In fact, the quark model analysis with
  appropriate multi-quark
• potential clarifies whether each exotic hadron
  exists or not,
• gives the properties of multi-quark hadrons, and
• predicts new-type exotic hadrons theoretically.
• We perform first study of multi-quark potential
  in lattice QCD.

-
-
34
First Lattice QCD Study for Static Quark
Potential in Multi-Quark System
Okiharu, H.S. et al. PRL 94 (2005) 192001
Okiharu, H.S. et al. PRD72 (2005) 014505
anti-quark
quark
?
4 quark system
quark
anti-quark
What Shape of Color Flux? Confining Force?
35
First Lattice QCD Study for Static Quark
Potential in Multi-Quark System
Okiharu, H.S. et al. PRL 94 (2005) 192001
Okiharu, H.S. et al. PRD72 (2005) 014505
What Shape of Color Flux? Confining Force?
quark
quark
?
5 quark system
anti-quark
quark
quark
36
First Lattice QCD Study for Static Quark
Potential in Multi-Quark System
Okiharu, H.S. et al. PRL 94 (2005) 192001
Okiharu, H.S. et al. PRD72 (2005) 014505
We formulate Multi-Quark Wilson Loops.
anti-quark
quark
4 quark system
quark
anti-quark
4 Quark Wilson Loop
quark
quark
5 quark system
anti-quark
quark
quark
1 T
VNQ(r) -lim lnltWNQgtT
5 Quark Wilson Loop
T?8
The Multi-Quark potentials can be obtained from
the corresponding Multi-Quark Wilson Loops.
37
First Lattice QCD Study for Static Quark
Potential in Multi-Quark System
Okiharu, H.S. et al. PRL 94 (2005) 192001
Okiharu, H.S. et al. PRD72 (2005) 014505
anti-quark
quark
4 quark system
VNQ(r)
quark
anti-quark
N4,5
quark
quark
5 quark system
anti-quark
quark
quark
Partial lattice QCD data of Multi-quark potential
For more than 200 different patterns of
multi-quark configurations, we have accurately
performed the first lattice QCD calculations for
multi-quark potentials.
38
First Lattice QCD Study for Static Quark
Potential in Multi-Quark System
Okiharu, H.S. et al. PRL 94 (2005) 192001
Okiharu, H.S. et al. PRD72 (2005) 014505
anti-quark
quark
4 quark system
VNQ(r)
quark
anti-quark
N4,5
color flux tube
quark
quark
5 quark system
anti-quark
quark
quark
Partial lattice QCD data of Multi-quark potential
For more than 200 different patterns of
multi-quark configurations, we have accurately
performed the first lattice QCD calculations for
multi-quark potentials.
39
First Lattice QCD Study for Static Quark
Potential in Multi-Quark System
Okiharu, H.S. et al. PRL 94 (2005) 192001
Okiharu, H.S. et al. PRD72 (2005) 014505
anti-quark
quark
4 quark system
VNQ(r)
quark
anti-quark
N4,5
color flux tube
quark
quark
5 quark system
anti-quark
quark
quark
Partial lattice QCD data of Multi-quark potential
For more than 200 different patterns of
multi-quark configurations, we have accurately
performed the first lattice QCD calculations for
multi-quark potentials.
40
First Lattice QCD Study for Static Quark
Potential in Multi-Quark System
Okiharu, H.S. et al. PRL 94 (2005) 192001
Okiharu, H.S. et al. PRD72 (2005) 014505
anti-quark
quark
4 quark system
VNQ(r)
quark
anti-quark
N4,5
color flux tube
quark
quark
5 quark system
anti-quark
quark
quark
Lmin total length of string linking the N
valence quarks
g2 4p
N
TiaTja ri - rj
VNQ(r) ? sLmin
iltj
One-Gluon-Exchange Coulomb potential
Linear potential based on string picture
41
Okiharu, H.S. et al. PRD72 (2005) 014505
h
2d
42
Summary of the First Part Static Potentials

• We have performed the first accurate Lattice QCD
  studies for
• static multi-quark (3Q, 4Q, 5Q) potentials.
• The multi-quark potential is well described by
• OGE Coulomb String-picture Linear Confinement
  Potential.

Lmin total length of string linking the N
valence quarks
g2 4p
N
TiaTja ri - rj
VNQ(r) ? sLmin
iltj
One-Gluon-Exchange Coulomb potential
Linear potential based on string picture
We have found the Universality of Quark
Confinement Force (String Tension) in hadrons
sQQ s3Q s4Q s5Q
-
43
Heavy-Heavy-Light Quark Potential and
Light-quark Effects to Inter-two-quark
Interaction in BaryonsSU(3) Lattice QCD and
Analytical Model Calculation
So far, we have obtained the definite conclusions
for the static inter-quark potentials in QCD.
However, in the real world, the quark mass is
finite and quarks are moving inside hadrons.
Here, we investigate the effect of the quark
motion to the inter-two-quark interaction in
baryons. To this end, we study the idealized
situation of heavy-heavy-light quark systems
where two heavy quarks can be treated as static
quarks.
So far, we have obtained the definite conclusions
for the static inter-quark potentials in QCD.
However, in the real world, the quark mass is
finite and quarks are moving inside hadrons.
Here, we investigate the effect of the quark
motion to the inter-two-quark interaction in
baryons. To this end, we study the idealized
situation of heavy-heavy-light quark systems
(QQq systems) where two heavy quarks can be
treated as static quarks. This situation
physically corresponds to doubly charmed
baryon as .
idealize
static quarks
44
Doubly charmed baryon

• In 2002, the first doubly charmed baryon
  was
• experimentally observed at SELEX, Fermilab.

M. Mattson et al., Phys. Rev. Lett. 89, 112001
(2002). A. Ocherashvili et al., Phys. Rev. Lett.
B628, 18 (2005).
Theoretical calculations for the doubly charmed
baryons
R. Lewis et al., Phys. Rev. D 64, 094509
(2001). N. Mathur et al., Phys. Rev. D 66, 014502
(2002).
Lattice QCD
A. D. Rujula et al., Phys. Rev. D 12, 147 (1975).
Potential model
45
Doubly charmed baryon (experiment)

• The first experimental observation at SELEX,
  Fermilab
• 600 GeV/c charged hyperon beam

2
Mass 3519 1 MeV/c
M. Mattson et al., Phys. Rev. Lett. 89,
112001 (2002).
46
W. M. Yao et al., J. Phys. G 33, 1
(2006).
47
W. M. Yao et al., J. Phys. G 33, 1
(2006).
48
Heavy-heavy-light quark (QQq) potential

• The situation is idealized as
• Two heavy quarks (Q) ? Two static quarks (MQ?8)
• One light quark (q) ? finite-mass quark (Mq
  various value)
• The QQq potential VQQq(R) is defined as the
  energy of
• QQq systems in terms of the inter-heavy-quark
  distance R.

One light quark is moving around Two Static Quarks
We calculate the QQq potential VQQq(R) in Lattice
QCD and also in a non-relativistic potential
model.
49
QQq potential in Lattice QCD
The QQq Wilson loop is defined as
light-quark propagator
The QQq potential is obtained as
cf) 3Q Wilson loop for static 3Q potential
50
Lattice QCD Simulation Conditions

• Standard plaquette gauge action
• ß 6.0 (lattice spacing a 0.10 fm)
• 164 isotropic lattice
• Quenched calculation
• O(a)-improved clover fermion action
• ?0.1200, 0.1300, 0.1340, 0.1380
• Wall-source wall-sink propagator
• Calculated on NEC-SX8R at RCNP, Osaka Univ.

Constituent quark mass Mq m?/2
51
Lattice QCD Result for QQq potential
The QQq potential VQQq(R) can be well fitted by
a Coulomb linear type potential
The Coulomb coefficient Aeff is almost the same.
cf.) Static 3Q in lattice QCD Takahashi, H.S.
et al., PRD 65, 114509 (2002).
The effective string tension between two heavy
quarks is about 20 reduced.
52
QQq Potential in the Potential Model
We start from Non-relativistic Hamiltonian for
heavy-heavy-light quark (QQq) system
using the static 3Q potential from the lattice
QCD result
the color flux-tube length
Takahashi, H.S. et al., Phys. Rev. D 65, 114509
(2002).
Note that, in the static limit of two heavy
quarks, spin-dependent interactions proportional
to 1/MQ disappear.
We calculate the light-quark wave function from
this Hamiltonian, using the energy variational
calculation in discretized space.
53
?
Confinement potential in Baryons
Confinement potential
If all angles of the 3Q triangle lt 120
Z
?
If an angle of the 3Q triangle gt 120
Z
Takahashi, H.S. et al., Phys. Rev. D 65, 114509
(2002).
54
Renormalization-group inspired variational method
To get the light-quark wave function, we perform
the energy variational calculation in discretized
space.
Here, we use the renormalized-group (RG) inspired
variational method
Starting from a coarse lattice, we proceed the
variational calculation to the finer mesh lattice
iteratively.
55
Light-quark spatial distribution
The light-quark probability ?q2 around the Two
Static Quarks. Brighter region denotes higher
probability of the light-quark.
56
Lattice QCD Result
Potential Model Result
cf.) Static 3Q in lattice QCD Takahashi, H.S.
et al., PRD 65, 114509 (2002).
The QQq potential is well fitted by
We find again about 20 reduction of the
effective string tension between two heavy
quarks.
57
Effective String Tension between two heavy
quarks
String tension
Effective string tension
One reason for the reduction of the effective
string tension between two heavy quarks is the
geometrical difference between the
inter-heavy-quark distance R and the flux-tube
length Lmin.
58
Summary and Concluding Remarks

• We have perform the first study for the QQq
  potential in SU(3) lattice QCD with O(a)-improved
  clover action and in the non-relativistic
  potential model.
• We have used a Renormalization Group (RG)
  inspired variational calculation for the
  calculation of light-quark wave function in the
  potential model.
• The effective string tension between two heavy
  quarks is significantly reduced in comparison
  with the ordinary string tension of the static 3Q
  case.

59
Light-quark Effects for Effective Reduction of
Confining Force between Two Quarks in Baryons
H. Suganuma, A. Yamamoto, H. Iida (Kyoto Univ.)
1. Heavy-heavy-light quark potential in SU(3)
lattice QCD A. Yamamoto, H. Suganuma, H.
Iida, arXiv0708.3610 hep-lat Abstract We
perform the first study for the heavy-heavy-light
quark (QQq) potential in SU(3) lattice QCD at the
quenched level. We calculate the energy of QQq
systems as the function of the distance R between
the two heavy quarks, and find that the QQq
potential VQQq(R) is well described with a
Coulomb plus linear potential form. Compared with
the static three-quark case, the effective string
tension between the heavy quarks is significantly
reduced by the light-quark effect. 2. Light-quark
effects on the inter-quark potential in baryons
A. Yamamoto, H. Suganuma, arXiv0709.0171
hep-ph Abstract We also study the QQq system
in a non-relativistic potential model with the
static three-quark potential which is obtained by
lattice QCD. Using a renormalization-group-inspire
d variational method in discretized space, we
calculate the ground-state energy of QQq systems
and the light-quark spatial distribution. We find
that the effective string tension between the
heavy quarks is reduced compared to the static
three-quark case. We conjecture that the
effective reduction of the inter-two-quark
confining force is induced by the remaining
3rdquark in light-quark baryons.