Unpolarized and polarized elementary kaon electroproduction at MAMI
Structure of the (1405) and kaon-nucleon dynamics
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1 2009, May 11th Tokyo Institute of Technology a Tetsuo Hyodo a Structure of the Λ(1405) and kaon-nucleon dynamics supported by Global Center of Excellence Program “Nanoscience and Quantum Physics”
Transcript of Structure of the (1405) and kaon-nucleon dynamics
12009, May 11th
Tokyo Institute of Technologya
Tetsuo Hyodoa
Structure of the Λ(1405) and kaon-nucleon dynamics
supported by Global Center of Excellence Program“Nanoscience and Quantum Physics”
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Contents
Chiral unitary approachStructure of Λ(1405)
Effective single-channel KN interaction
On the KNN (strange dibaryon) system
Contents
T. Hyodo and W. Weise, Phys. Rev. C 77, 035204 (2008)
T. Hyodo, D. Jido, L. Roca, Phys. Rev. D77, 056010 (2008). L. Roca, T. Hyodo, D. Jido, Nucl. Phys. A809, 65 (2008).
T. Hyodo, D. Jido, A. Hosaka, Phys. Rev. C78, 025203 (2008).
・Nc Behavior and quark structure
・Dynamical or CDD pole (genuine quark state) ?
・Electromagnetic propertiesT. Sekihara, T. Hyodo, D. Jido, Phys. Lett. B669, 133-138 (2008).
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Description of S = -1, KN s-wave scattering : Λ(1405) in I=0Chiral dynamics
- Interaction <-- chiral symmetry
- Amplitude <-- unitarity (coupled channel)R.H. Dalitz, T.C. Wong, G. Rajasekaran, PR153, 1617 (1967)
Y. Tomozawa, Nuovo Cim. 46A, 707 (1966); S. Weinberg, Phys. Rev. Lett. 17, 616 (1966)
Introduction
T =1
1− V GV
T
= +T
N. Kaiser, P. B. Siegel, W. Weise, Nucl. Phys. A594, 325 (1995),E. Oset, A. Ramos, Nucl. Phys. A635, 99 (1998),J. A. Oller, U. G. Meissner, Phys. Lett. B500, 263 (2001),M.F.M. Lutz, E. E. Kolomeitsev, Nucl. Phys. A700, 193 (2002), .... many others
works successfully, also in S=0 sector, meson-meson scattering sectors, systems including heavy quarks, ...
chiral
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T. Hyodo, S.I. Nam, D. Jido, A. Hosaka, Phys. Rev. C68, 018201 (2003),T. Hyodo, S.I. Nam, D. Jido, A. Hosaka, Prog. Theor. Phys. 112, 73 (2004)
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150
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0
!T [
mb]
300200100
K-p
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0300200100
"0#
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0300200100
"+$%
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!T [
mb]
300200100Plab [MeV/c]
K0n
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0300200100
Plab [MeV/c]
"0$0
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Plab [MeV/c]
"%$+
How it works? vs experimental dataChiral unitary approach
14401420140013801360s [MeV]
!" m
ass d
istrib
utio
n
γ Rc Rn
exp. 2.36 0.664 0.189
theo. 1.80 0.624 0.225
Total cross sections threshold ratios
πΣ spectrum
==> KN interaction in this framework
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Two poles for one resonancePoles of the amplitude in the complex plane : resonance
∼
Tij(√
s) ∼ gigj√s − MR + iΓR/2
Real part MassImaginary part Width/2
Residues Couplings
1360
1380
1400
1420
1440
-20
-40
-60
-80
0.5
1.0
1.5
0.5
1.0
1.5
!(1405)
Re[z]Im[z]
|T|
|Λ(1405)〉 = + b|Λ∗2〉a|Λ∗
1〉D. Jido, J.A. Oller, E. Oset, A. Ramos, U.G. Meissner, Nucl. Phys. A 723, 205 (2003);T. Hyodo, W. Weise, Phys. Rev. C 77, 035204 (2008)
Physical state: superposition
Chiral unitary approach
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Dynamical state and CDD poleResonances in two-body scattering・Knowledge of interaction (potential)
(b) CDD pole: elementary, independent, ...
(a) dynamical state: molecule, quasi-bound, ...
L. Castillejo, R.H. Dalitz, F.J. Dyson, Phys. Rev. 101, 453 (1956)
・Experimental data (cross section, phase shift,...)
Resonances in chiral unitary approach -> (a) dynamical?
Structure of Λ(1405) resonance
MB
e.g.) Deuteron in NN, positronium in e+e-, (σ in π π), ...
e.g.) J/Ψ in e+e-, (ρ in π π), ...
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CDD pole contribution in chiral unitary approachAmplitude in chiral unitary model
Known CDD pole contribution(1) Explicit resonance field in V(2) Contracted resonance propagator in V
V : interaction kernel (potential)G : loop integral (Greenʼs function)
Defining “natural renormalization scheme”, we find CDD pole contribution in G (subtraction constant).
Structure of Λ(1405) resonance
T. Hyodo, D. Jido, A. Hosaka, Phys. Rev. C78, 025203 (2008).
N(1535) in πN scattering --> dynamical + CDD poleΛ(1405) in KN scattering --> mostly dynamical !"#
!$#
!%#
!&#
#'()*)+,
-./
0$1#0$##011#01##0%1#0%##021#3-)*)+,-./
*0!4)5)!60%#17
*84)5)8601217
*&!4)5)!60%#17
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Nc scaling in the modelNc : number of color in QCDHadron effective theory / quark structure
The Nc behavior is known from the general argument.<-- introducing Nc dependence in the model, analyze the resonance properties with respect to NcJ.R. Pelaez, Phys. Rev. Lett. 92, 102001 (2004)
Nc scaling of (excited) qqq baryon
-250-200-150-100
-500
Im W
[MeV
]2001000-100
Re W - MN - mK [MeV]
z1(Nc=3)
z2(Nc=3)
z2(12)
z1(12)
Result : ~ non-qqq (i.e. dynamical) structure
T. Hyodo, D. Jido, L. Roca, Phys. Rev. D77, 056010 (2008). L. Roca, T. Hyodo, D. Jido, Nucl. Phys. A809, 65 (2008).
Structure of Λ(1405) resonance
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Electromagnetic propertiesAttaching photon to resonance--> em properties : rms, form factors,...
Structure of Λ(1405) resonance
large (em) size of the Λ(1405) : c.f. -0.12 [fm2] for neutron--> meson-baryon picture
T. Sekihara, T. Hyodo, D. Jido, Phys. Lett. B669, 133-138 (2008).
result of mean squared radii :|〈r2〉E| = 0.33 [fm2]
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Summary 1 : Structure of Λ(1405)
Dynamical or CDD?
Analysis of Nc scaling
Electromagnetic properties
=> dominance of the MB components
=> large e.m. size
We study the structure of the Λ(1405)
=> non-qqq structure
Structure of Λ(1405) resonance
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Summary 1 : Structure of Λ(1405)
Dynamical or CDD?
Analysis of Nc scaling
Electromagnetic properties
Independent analyses consistently support the meson-baryon molecule picture of the Λ(1405)
=> dominance of the MB components
=> large e.m. size
We study the structure of the Λ(1405)
=> non-qqq structure
Structure of Λ(1405) resonance
MB
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Effective single-channel KN interaction
Effective interaction based on chiral SU(3) dynamics
Coupled-channel BS eq. + real valued interaction
Result of chiral dynamics --> single channel potential
few-body K-nuclei
(exact transformation)
Single-channel BS eq.+ complex interaction
(with approximation)
Schrödinger equation + local, complex, and energy-dependent potential
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2
0
-2
F KN
[fm
]
1440140013601320!s [MeV]
Re F, full
KN(I=0)
1.5
1.0
0.5
0.0
-0.5
-1.0
F !" [f
m]
1440140013601320!s [MeV]
!"(I=0)
Im F, full
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(Diagonal) scattering amplitude in KN and πΣEffective single-channel KN interaction
Binding energy : B = 15 MeV <--> 30 MeV
~1405 MeV
Resonance in KN channel : at around 1420 MeV<-- consequence of strong πΣ dynamics (coupled-channel)
~1420 MeV
Very strong attraction in KN (higher energy) --> bound stateStrong attraction in πΣ (lower energy) --> resonance
-120
-100
-80
-60
-40
-20
0
Im z
[MeV
]1440140013601320
Re z [MeV]
!" resonance
KN bound stateWithout off-diagonal
KNπΣ
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Origin of the two-pole structure
KN πΣ
Chiral interaction
-120
-100
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-40
-20
0
Im z
[MeV
]1440140013601320
Re z [MeV]
!" resonance
z2(full)
z1(full)
KN bound state
KNπΣ
Two poles : natural consequence of chiral interaction(pole position is model dependent)
Effective single-channel KN interaction
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Schematic illustration : AY vs Chiral
KN
πΣ
Feshbach resonance
Feshbach resonance on resonating continuum
continuum
bound state
Λ(1405)experiment
AY
Effective single-channel KN interaction
KN
πΣresonance
bound state
Chiral (Dalitzʼs coupled -channel model)
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Summary 1 : KN interactionWe study the consequence of chiral SU(3) dynamics in KN phenomenology.
Resonance structure in KN appears at around 1420 MeV <-- strong πΣ dynamicsTwo attractive interactions in KN and πΣ
Application to K-pp system (without πΣN)
Effective single-channel KN interaction
T. Hyodo and W. Weise, Phys. Rev. C 77, 035204 (2008)
Doté-san’s talk
--> two poles for the Λ(1405)--> weaker effective KN interaction
observed in ΛN inv. mass effect of decay channel coupling
-120
-100
-80
-60
-40
-20
0
Im z
[MeV
]
1440140013601320Re z [MeV]
!" resonance
z2(full)
z1(full)
KN bound state
KNπΣ
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Which channel is relevant?On the KNN (strange dibaryon) system
Theoretical studiesKNN - (πΣN) channels
πΣN
K̄NN
ΛN
ΣN
!"##
!$%
!&%
!"#$%
&"'(!)
πΛN
!&%
*+,-./ ,012
Experimental candidates- energy ≦ πΣN
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Λ*N state in chiral dynamicsChiral dynamics --> two Λ* states : Λ*1, Λ*2
On the KNN (strange dibaryon) system
|Λ(1405)〉 = a|Λ∗1〉 + b|Λ∗
2〉B=2 system : Λ*1N, Λ*2N ?
Y. Ikeda, RCNP workshop, Dec. 25, 2008
|B = 2, S = −1〉 = a′|Λ∗1N〉 + b′|Λ∗
2N〉
T. Uchino, T. Hyodo, M. Oka, in preparationlevel repulsion --> Λ*1N becomes light?
K̄NNΛ∗
1N
Λ∗2N
!"##$%&'()$*+
+
,-$./0/12 (/34$./0/12
5
5
**
mixing of Λ*1N <--> Λ*2N
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Summary 2 : KNN systemKNN or strange dibaryon system
To compare with observed candidates, we should choose relevant channel(s).
If there are two states for Λ*(1405), there could be two states in KNN-πΣN system
On the KNN (strange dibaryon) system
importance of πΣN channel?
Mixing of two Λ*--> level repulsion?
actual decay into ΛN channel--> change the spectrum?
