Transcript Multiquark Systems with Strangeness

Multiquark Systems with
Strangeness
Makoto Oka
岡 真
Tokyo Institute of Technology
SNP06
張家界, 中華人民共和国
September, 2006
Contents
1. Quark model for multiquark systems
ground states, excited states
scalar nonets, pentaquarks
2. Lattice QCD for exotics
pentaquarks
5-quark components of (1405)
3. QCD sum rules for exotics
mixings of exotic multi-quark components
4. Conclusion
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Quark model
Constituent quarks in hadrons
mesons qq
baryons qqq
exotics qqqq, qqqqq, . . .
Constituent quarks must be effective degrees of
freedom which are valid only in low energy
regime. They must have the same
"conserved charges" as the QCD quarks:
baryon 1/3, spin 1/2, color 3, flavor 3.
The constituent quarks have dynamical masses
induced by chiral sym breaking of QCD
vacuum m q ~ M B ~ 300  500 MeV / c 2
3
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Ground states
Ground-state mesons (PS+V nonets) and
baryons (8+10) are well described by the
quark model based on SU(3) x SU(2) -> SU(6)
mass spectrum
em-weak properties, ex. magnetic moments
Required (minimum) dynamics consists of
confinement + color-magnetic interactions.
with a few exceptions
“ problem” -> chiral symmetry
“ ' problem” -> UA(1) anomaly
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Excited states: Scalar mesons
“Quark-shell-model” based on SU(6) x O(3)
encounters difficulties for excited states.
scalar meson nonets: 3P0: 0++
0+: (~600), f0(980), a0(980),  (900)*
The ordering is not "natural" as a qq nonet.
 ~ (uu  dd ) /

2 ; a 0 ~ (uu  dd ) /
2;
f 0 ~ ss
expected
m() ~ m(a0) < m(f0)
observed
m() < m(a0) ~ m(f0)
No spin-orbit partners in the vicinity: 3PJ: 1+, 2+
* (900) : indicated in K final states of J/ and
D meson decays, but not yet established.
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Scalar mesons as tetra-quark states
A possible explanation is to consider them as exotic
tetra-quark states.
 ~ SS  (ud )( u d )
a 0 ~ (U U  D D ) /
2  (( ds )( d s )  ( su )( s u )) /
2
f 0 ~ (U U  D D ) /
2  (( ds )( d s )  ( su )( s u )) /
2
composed of diquarks in flavor 3
U  ( d s ) S  0,C  3


D  (s u ) S  0,C  3
S  (u d ) S  0,C  3
Then the expected spectrum from strange quark
counting is
m() < m(a0) ~ m(f0)
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

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Exotic multi-quark systems
Multi-quark components may help to explain
anomalies in the excited hadron spectrum.
ex. scalar nonets, (1405), X(3872)
Dynamics: Why is (1405) likely to be 5q?
(1405) J= 1/2-, flavor singlet
☆ uds L=1 orbital excited states with spin 1/2
=> J=1/2- and 3/2☆ udsuu, . . L=0 ground state
(ud)(su) u . .
s=0 s=0
S=1/2 => J=1/2 isolated
diquarks
(1520) 3/2Tokyo Tech
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Exotic multi-quark systems
Necessary techniques have been developed in
studying purely exotic hadrons.
+ B=1, S=1, Y=2
-- Y=-1, I=3/2
+
--
+
Nakano et al., LEPS@SPring-8 (2003)
M 1540 MeV with  1 MeV or less
B=1, S=+1, 5-quark ( u2d2s ) bound state
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Quark Models for Pentaquark +
How does the known dynamics of the quark
model work for +?
 "shell-model" approaches (+ correlations)
Carlson et al, Jaffe-Wilczek, Karliner-Lipkin,
Jennings-Maltman, Bijker et al
 variational approaches
Takeuchi-Shimizu, Hiyama et al, Stancu et al,
Matsumura et al,
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Quark Models for Pentaquark +
A variational method calculation
by Takeuchi, Shimizu (2006)
models
Large + mass, small splitting of 1/2 and 3/2
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Quark Models for Pentaquark +
Variational solution of 5 quark system coupled
to NK continuum states
E. Hiyama et al. PLB633 (2006)
L=0
NK threshold
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L=1
NK threshold
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So, . . .
The quark model is based on the chiral symmetrybroken QCD, which contains massive quarks as
effective degrees of freedom.
The quark model describes most ground state
mesons and baryons fairly well.
The quark model, however, is less effective for
excited mesons and baryons. Some of the
discrepancies (scalar mesons, (1405), ...) suggest
exotic multiquark components.
The pentaquark + is a mystery.
No honest calculation reproduces its mass and
width simultaneously.
The similar calculations are underway for various
multi-quark candidates.
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QCD
QCD is the theory of hadrons.
It does not a priori exclude exotic multi-quark
bound (resonance) states (as far as they are
color-singlet).
Direct applications of QCD to exotics are
desperately needed.
Lattice QCD
QCD sum rules
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Lattice QCD
Lattice QCD is powerful in understanding nonperturbative physics of QCD:
vacuum structure, phase diagrams, mass spectra of
ground state mesons and baryons, interactions of
quarks, . . .
Lattice QCD has two (severe) restrictions:
Light quarks are too expensive. It requires (often
drastic) extrapolation from large-quark-mass
simulations.
No direct access to resonance poles is possible.
It is hard to distinguish resonances from hadron
scattering states. Real number simulations can not
access complex poles.
Applications to exotic hadrons are yet limited.
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LQCD for Pentaquark +
Quenched LQCD for + (J = 1/2)
Csikor, Sasaki, Chiu, Mathur, Ishii, Alexandrou, Takahashi,
Lasscock, Holland, Negele, . . .
Quenched LQCD for + (J = 3/2)
Lasscock, Ishii
Anisotropic Lattice QCD studies of + (J = 1/2 and 3/2)
Ishii et al., PRD 71 (2005) 034001
Ishii et al., PRD 72 (2005) 074503
lattice size 123×96, β = 5.75 : (2.2fm)3×4.4fm in phys. unit
anisotropic lattice (as/at=4), 504 configurations
O(a) improved clover Wilson quark
with quark mass mu, d = ms to 2ms
(linearly) extrapolated to the physical mass
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Summary of LQCD results for +
J =1/2 diquark-operator (DQ)
1/2– 1.75 GeV: consistent with NK(L=0) scatt.
The Hybrid b.c. method rejects 5Q states.
1/2+ 2.25 GeV: heavy
J =3/2 DQ, NK*, color-twisted NK* opearators
3/2– 2.11 GeV: consistent with NK (L=0) thres.
3/2+ 2.42 GeV: consistent with NK (L=1) thres.
3/2+ 2.64 GeV: consistent with N K L=0) thres.
No candidate for compact 5Q state is found.
Most LQCD parties agree with these results.
The QCD sum rules give the consistent results.
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J = 1/2  pentaquark
Ishii et al., PRD 71 (2005) 034001
After the chiral extrapolation
(1) Positive parity: 2.25(11) GeV
(2) Negative parity: 1.75(3) GeV
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Exotic multi-quark components
How do we study the exotic multi-quark
components of hadrons in QCD?
Quenched Lattice QCD
 (1405 )  uds ( 3 Q )  N K ( 5 Q )  
  uds
(3Q operator)
3Q is dominant in
quenched LQCD
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  pK

 nK
0
(5Q operator)
5Q-dominant diagram
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(1405) with 3Q operators
Y. Nemoto et al., PRD68, 094505(2003)
W. Melnitchouk et al., PRD67, 114506 (2003)
F.X. Lee et al., NPB(PS)119, 296(2003) [LATTICE2002]
T. Burch et al., hep-lat/0604019.
Large discrepancy between the lattice prediction and the
observed mass of Λ(1405) (about 300 MeV)
Y. Nemoto et al., PRD68, 094505(2003)
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(1405) with 5Q operator
Technical problem to be solved
Spectrum in Λ(1405) channel
It is difficult to separate (1405) from the
NK threshold (scattering states).
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Hybrid BC method: Twist Spatial BC
N.Ishii, T.Doi, H.Suganuma, MO
★ Conventional BC
Periodic BC(PBC)
★ Twisted BC
“Hybrid BC” ( “HBC” )
u, d , s
u, d , s
u, d, s
PBC
u, d, s
anti PBC
PBC
(L～２fm is assumed)
“HBC” will enable to isolate Λ(1405).
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note: ”HBC” is valid
only in the limit where
qq anihilation can be
neglected.
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HBC method for +
Twist spatial BC for u, d quarks
Ishii et al., PRD71 (2005) , PRD72 (2005)
u quark anti-periodic BC
d quark anti-periodic BC
s quark periodic BC

 (J


1 
2
)
NK(s-wave) threshold
No compact 5q resonance of J=1/2- was found.
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m(N) + m(Kbar)
5-quark component of Λ (1405)
m(Σ) + m(π)
chiral extrapl.
The chiral extrapolation
3Q operator
m3Q = 1.79(8) GeV
5Q operator
m5Q = 1.63(7) GeV ～ m(N)+m(K) [on lattice]
The preliminary result suggests that Λ(1405) is
dominated by 5Q.
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Exotic multiquark components
How large is the mixing probability of the exotic multi-quark
components?
There is NO well-defined mixing prob. in the field theory,
because there exists no conserved current corresponding
to the number of quarks: N(q)+N(q).
It depends on the choice of the quark operator.
Nevertheless, there are a set of well-defined quantities,
which might be useful in connecting the quark model
description
although they depend on the definition (normalization) of
the operators.
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"mixing angle"
Then one can evaluate the "mixing angle":
☆ QCD sum rule is applied.
a. 4-quark components of a0(I=1; 0+) meson
b. 5-quark components of (singlet; 1/2-) baryon
T. Nakamura, J. Sugiyama, T. Nishikawa, N. Ishii, M.O.
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Example: scalar a0
A set of interpolating fields
Define a genuine 4-quark operator J4’ so that J2
component of J4 is subtracted.
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QCD Sum Rule for scalar mesons
qq vs 4-quark in a0 meson
qq + 4-quark
pure 4-quark
qq
We conclude that the "4-quark component" is
dominant in the scalar meson a0.
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Conclusion
A technique using the hybrid boundary conditions
seems to work in lattice QCD to distinguish compact
states from scattering states.
The quenched LQCD suggests that (1405) is
predominantly a 5-quark state.
The mixing of the multi-quark components are not
well-defined from the field theoretical viewpoint.
However, one can define a set of useful mixing
amplitudes using the well-defined matrix elements of
local operators. Whether this definition of the mixing
is relevant in the quark model is yet an open problem.
The QCD sum rule indicates a large 4-q components
in scalar mesons.
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