1. Hadron spectroscopy Pentaquarks and baryon resonances
Atsushi Hosaka, RCNP Osaka Univ.
• Baryon resonances
Quark model description (deformed oscillator)
KN for L(1405) ~ importance of qq correlation
qq vs qq
Chiral symmetry
• Pentaquarks
Full 5-body calculation ~ qq
Production of Q+ ~ consistency of J-Lab and LEPS
Nov Dec. 2, 2005
J-PARC workshop, KEK

2. At low energies Lattice QCD does a lot:
Masses, Form factors, Resonances, (Interactions)
qq potential, Vacuum properties
Exotics (pentaquarks,…)?
Are there simple way to understand them?
Global/local symmetry and its breaking
Relevant degrees of freedom, effective interactions
ElementaryExcitation of non-perturbative vacuum (Kunihiro)
=> Models of QCD hopefully with one or at most few
But current understanding is not at this level
Nov Dec. 2, 2005
J-PARC workshop, KEK

3. Let us start with Quark model
Simple setups:
• SU(6) and small ms breaking
• Harmonic oscillator potential, V(r) = kr2
• Effective residual interaction
Gluons, Chiral mesons, instantons, …
To test the quark model, let us see baryon states
Nov Dec. 2, 2005
J-PARC workshop, KEK

4. Light flavor (uds) baryons
But if we rearrange
Well established states
49 ***,**** states out of 50
13 * , ** states out of 31
62 states
out of 81 states
Nov Dec. 2, 2005
J-PARC workshop, KEK

5. Positive parity baryons
• Measured from the ground state
• 8MS states are shifted downward by 200 MeV
Nov Dec. 2, 2005
J-PARC workshop, KEK

6. Negative parity baryons
• Measured from the 1/2+ ground state
• 48MS states are shifted downward by 200 MeV
Nov Dec. 2, 2005
J-PARC workshop, KEK

7. Deformed Oscillator Model
Takayama-Toki-Hosaka
Prog.Theor.Phys.101: ,1999
• Ground state: spherical
• Excited states:
Single particle excitation deforms the confining potential
Deformed states rotate collectively
=> Resonances as collectively rotated states
Nov Dec. 2, 2005
J-PARC workshop, KEK

8. It seems that we make a good job
BUT: Is this the end of the story???
Important questions:
• Quark correlations qq or qq
Roper as a diquark states => Nagata
• Also qqq* states can mix with qqq(qq)
L(1520) as a KN state => Hyodo
• Chiral symmetry
Nov Dec. 2, 2005
J-PARC workshop, KEK

9. Role of qq (meson)correlation
Meson clouds
Long time being said, but renewed interests
due to chiral perturbation and its unitarization
Interaction
Resonance
L Tomozawa-Weinberg
Basic assumptions:
Ground state hadrons as building blocks: B and M
Contact MB interaction dominates the s-wave dynamics
Nov Dec. 2, 2005
J-PARC workshop, KEK

10. L(1405) The state is crucially important for the K-nuclei
Jido-Oller-Oset-Ramos-Meissner,
Nucl.Phys.A725: ,2003: nucl-th/
The state is crucially important for the K-nuclei
KN ~ 8 x 8 = 1, 8, 8, 10, 10, 27
attractive
repulsive
Two poles near Mass ~ 1405
i (KN)
i (pS)
pS -> pS
KN -> pS
K–p –> ppS, Magas-Oset-Ramos, Phys.Rev.Lett.95:052301,2005
Nov Dec. 2, 2005
J-PARC workshop, KEK

11. In the quark language qq-correlation vs. qq-correlation
Color-spin interaction
qq(C, S) (3*C, 0S) (3*C, 1S) (6C, 0S) (6C, 1S)
–1/ / / –1/12
qq(C, S) (1C, 0S) (1C, 1S) (8C, 0S) (8C, 1S)
– / / –1/24
qq correlation is equally or more important than qq
for equal masses. If m>>m, then qq is suppressed
To see qq correlations, heavy quark systems may be suited
Nov Dec. 2, 2005
J-PARC workshop, KEK

12. Chiral symmetry Conventional wisdom:
• Chiral symmetry is spontaneously broken
• <qq> condenses
• Quarks couples to <qq> and obtain a constituent mass
Questions:
• What is the coupling of hadrons to <qq> ~ Hadron mass
• What are chiral (parity) partners
• What is the realization of chiral symmetry
Linear vs. non-linear
Nov Dec. 2, 2005
J-PARC workshop, KEK

13. They are related to: How far our world is from the symmetric world
How strongly chiral symmetry is broken
Large fp , ms
Small fp , ms
Nov Dec. 2, 2005
J-PARC workshop, KEK

14. If symmetry breaking is not very large
=> Particles in chiral group representations
SU(2)L x SU(2)R
Baryons: (1/2, 0), (1, 1/2), (3/2, 0), ….
N N, D, D,
with mixings
Mesons: (0, 0), (1/2, 1/2), (1, 0), …
s , s, p, r, a1
• For baryons, chiral partners can be made by
Particles of the same parity (N, D, R)
S. Weinberg, Phys.Rev.177: , 1969
Particles of opposite parities (N, N*)
Jido-Hosaka-Oka, Prog.Theor.Phys.106: ,2001
Jido-Hatsuda-Kunihiro, Phys.Rev.Lett.84:3252,2000
Nov Dec. 2, 2005
J-PARC workshop, KEK

15. • There could be N* of gA < 0
• gA ~ 1.25 close to 1
=> N ~ (1/2, 0) + (1, 1/2)
• There could be N* of gA < 0
• Masses of chiral partners degenerate
as symmetry recovers
BUT we need more
studies to clarify the
role of chiral symmetry
Nov Dec. 2, 2005
J-PARC workshop, KEK

16. Pentaquarks
Nov Dec. 2, 2005
J-PARC workshop, KEK

17. 5-body calculation for Q+
Hiyama et al, hep-ph/
Most serious calculation for 5-body system
with scattering states included
Gaussian expansion method +
Q+-confined
NK-scattering
Compute phase shifts qq
Nov Dec. 2, 2005
J-PARC workshop, KEK

18. Hamiltonian NR quark model of Isgur-Karl Nov. 30 - Dec. 2, 2005
J-PARC workshop, KEK

19. KN-phase shifts 1/2+ Eres ~ 530 MeV Gres ~ 110 MeV • Mass is too high
• Strong qs correlation –> JW configuration is suppressed
Diquark formation is a dynamical problem
Nov Dec. 2, 2005
J-PARC workshop, KEK

20. Production
Nov Dec. 2, 2005
J-PARC workshop, KEK

21. LEPS J-Lab g d -> K+ K– p n g n -> n K+ K– g p –> n K+ K0
CLAS g11
Preliminary
g10
g d --> K+ K- p (n) ?
J-Lab
Nov Dec. 2, 2005
J-PARC workshop, KEK

22. LEPS has observed but CLAS does not
Observation 1
LEPS: forward angle region
CLAS: side
J-Lab
LEPS
Beam line
Nov Dec. 2, 2005
J-PARC workshop, KEK

23. (Charge exchange) >> (Charge non-exchange)
Observation 2
Nam-Hosaka-Kim, hep-ph/ , PRD, 71:114012,2005
hep-ph/
• Large p, n asymmetry
(Charge exchange) >> (Charge non-exchange)
• Strongly forward peaking
Nov Dec. 2, 2005
J-PARC workshop, KEK

24. Effective Lagrangian approachu s t
contact
present only for charge exchange
n –> Q+ or p –> L(1520)
Nov Dec. 2, 2005
J-PARC workshop, KEK

25. Before the Q-production
gn -> K– L(1520) and gp -> K0 L(1520)
was studied and large pn asymmetry was known to us
Nam-Hosaka-Kim, hep-ph/ to appear PRD
Energy dependence
t (or q) dependence
Nov Dec. 2, 2005
J-PARC workshop, KEK

26. L(1520) JP = 3/2– g p –> K+ L(1520) Charge exchange
L = 700 MeV <=> r ~ 0.8 fm
Contact term
• Large pn asymmetry
• Strong forward peak
• Polarization??
To be checked by
experiments
Nov Dec. 2, 2005
J-PARC workshop, KEK

27. For Q+ g n –> K– Q+ Charge exchange
G = 1 MeV, L = 700 MeV <=> r ~ 0.8 fm
The total cross section is very sensitive to L
• Large pn asymmetry
• If Q+ is larger in size,
s may be smaller and strongly forward peaking
• s ~ few nb or less -> consistent with the CLAS result
Nov Dec. 2, 2005
J-PARC workshop, KEK

28. Summary • Hadrons seem to need different ingredients:
constituent quarks, diquarks, mesons, chiral symmetries.
• Perhaps we need a simple setup
having a predictive power, consistent with QCD, and
explaining ground to resonant states, decay/productions,…
• Pentaquarks may still survive, which should be explained by
the same setup
• Experimentally: exotics containing multi-quarks and antiquarks
are good laboratory to study the relevant questions.
Nov Dec. 2, 2005
J-PARC workshop, KEK

29. Nov Dec. 2, 2005
J-PARC workshop, KEK

30. Why hadrons? Everybody knows that:
• The core of matter (made of atoms)
• Strongly interacting quantum system of QCD
• Rich aspects in phase structure
They are based on:
hadron structure and reactions from quarks (QCD)
Nov Dec. 2, 2005
J-PARC workshop, KEK

31. But not so easy Due to non-perturbative dynamics
Color confinement and chiral symmetry breaking
Is it possible to describe hadron properties?
Can we predict masses, form factors,
decay/production rates and so on?
Can we predict unknown states prior to experiment?
Nov Dec. 2, 2005
J-PARC workshop, KEK

32. Theta production, JP = 3/2 Total s Log-scale Angular dist Log-scale
neutron ~ forward peak
Contact term
proton ~ rather flat
Nov Dec. 2, 2005
J-PARC workshop, KEK

33. Good for conventional baryons
Mass
Magnetic moments
Charge radii
Nov Dec. 2, 2005
J-PARC workshop, KEK

34. LEPS: deuteron -> (Theta, L(1520))
We need to understand g K
• Reaction mechanism
　　 Soft K? d N Q
MNK
• Elementary process Q+, L(1520) production
• Consistency between the J-Lab experiment
Nov Dec. 2, 2005
J-PARC workshop, KEK