Scalar LN and LL interaction within a chiral unitary approach
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Transcript of Scalar LN and LL interaction within a chiral unitary approach
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Scalar and interaction within a chiral unitary approach
HYP2006, Mainz,13th Oct 2006
Kenji Sasaki
E. Oset
M. J. Vicente Vacas(Valencia University - IFIC)
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Introduction• The scalar-isoscalar potential plays an important role in the nu
cleon-nucleon interaction providing an intermediate range attraction in all channels.
• In terms of the OBE, the intermediate attraction is brought by “”-exchange potential, but the nature of this particle has been a source of controversy.
What will be happen in N and interaction?HYP2006, Mainz,13th Oct 2006
• Using chiral unitary approach, the meson is dynamically generated as the meson-meson resonance.
• Applying this model to the NN interaction, the correlated two-pion interaction produces a moderate attraction as a “” meson at the intermediate range region, however it generates the repulsion at the medium range region.
E Oset, H Toki, M Mizobe, and T T Takahashi PTP103 (2000) 351
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Scalar baryon-baryon potential
Correlated Uncorrelated
One-meson exchange
Same physics in different formalism (dispersion relation,) done by the Julich group
J Haidenbauer and U G Meissner Phys Rev C72 (2005) 044005HYP2006, Mainz,13th Oct 2006
B1 B2
B1 B2
B1 B2
B1 B2
B1 B2
B1 B2
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Calculation of correlated two-meson potential
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Correlated two-meson potentialWe define the correlated two-meson exchange potential as
Triangle scalar loop contribution
HYP2006, Mainz,13th Oct 2006
T-matrix of meson-meson scattering
calculated by the chiral unitary method.
It reproduces the meson-meson phase shift up to 1.2GeV quite well.
Cancellation mechanism for off-shell part of meson-meson amplitude
•(E Oset, H Toki, M Mizobe, and T T Takahashi PTP103 (2000) 351 ).
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Diagrams of two-meson triangle loop
HYP2006, Mainz,13th Oct 2006
Meson-baryon (Octet) interaction
Meson-baryon (Decuplet) interaction
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Triangle scalar loop contribution
The contribution of the heavy meson loop is suppressed in the small momentum region.
q[MeV]
M=M m=m M=M m=m
N
N
K(q
)
0 500 1000 1500 2000 2500
2
4
6
8
HYP2006, Mainz,13th Oct 2006
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Two meson amplitude in scalar channelChiral Lagrangean for meson-meson interaction
Tree level amplitudes of meson-meson scattering
We can separate the off-shell part of amplitudes
HYP2006, Mainz,13th Oct 2006
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Unitarization of the amplitude
= +
Using the tree level interaction, V, as input, we solve the L-S type equation
The G is the meson-meson loop function
(The off-shell part of interaction gives the renormalization of physical values.)
J A Oller and E Oset, Nucl Phys A620 (1997) 438J A Oller E Oset and J R Pelaez Phys Rev D59 (1999) 074001
HYP2006, Mainz,13th Oct 2006
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Correlated two meson potential
2.5
Cor
T(q
)
q[MeV]0 500 1000 1500 2000 2500
0.5
1
1.5
2
(10-5)
HYP2006, Mainz,13th Oct 2006
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Calculation of uncorrelated two-meson potential
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Uncorrelated two-meson diagrams
HYP2006, Mainz,13th Oct 2006
Set of diagrams for N channel
Set of diagrams for channel
Ladder type diagram
Cross type diagram
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Uncorrelated two meson potential
Ladder type potential Cross type potential
q[MeV]0 500 1000 1500 2000 2500-8
-6
-4
-2
0
The ladder type (direct) potential is much stronger than the cross type potential
HYP2006, Mainz,13th Oct 2006
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Results of scalar N and potential
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Scalar N potential in momentum space
The correlated two-meson potential plays an important role around 500 MeV.
The two-kaon contribution is very small comparing with two-pion contribution.
Cor UnCor Omega Total
V(q
)[M
eV-2
]
q[MeV]
(10-5)
0 500 1000 1500 2000 2500-15
-10
-5
0
5
10
15
Cor UnCor Omega Total
V(q
)[M
eV-2
]q[MeV]
(10-5)
0 500 1000 1500 2000 2500-15
-10
-5
0
5
10
15
HYP2006, Mainz,13th Oct 2006
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Scalar N potential in configuration spaceV
(r)[
MeV
]
r[fm]
Cor UnCor Omega Total
0.5 1 1.5 2 2.5 3-100
-50
0
50
100
V(r
)[M
eV]
r[fm]
Cor UnCor Omega Total
0.5 1 1.5 2 2.5 3-100
-50
0
50
100
The two-kaon contribution is very small comparing with two-pion contribution.
The short range repulsion is produced by the correlated two-meson contribution.
The attraction is produced by both the corr. and uncor. two-meson contribution.
HYP2006, Mainz,13th Oct 2006
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Scalar potential in momentum space
HYP2006, Mainz,13th Oct 2006
The similar shape of potentials are produced
The potential is largely enhanced by the two-kaon contribution
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potential in configuration space
HYP2006, Mainz,13th Oct 2006
The two-kaon contribution is relatively stronger than the N case
Short range repulsion in total potential is smaller than the N case
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The exchange potential
The total exchange will be attractive in our calculation, but it is very weak.
HYP2006, Mainz,13th Oct 2006
The repulsive potential comes from the correlated meson diagrams
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Summary and conclusion• We calculate the scalar-isoscalar N and potential within
a chiral unitary approach.
• We found that the correlated two-meson exchange contribution generates a repulsive potential in the short range region in spite of an attractive potential in the long range region.
• Summing up the correlated and uncorrelated two-meson potential, they produce strong attraction, like -exchange.
• Two-kaon exchange contribution is quite small comparing with two-pion contribution in N channel, on the other hand, it has a large contribution in channel.
• The short range repulsive potential is generated by both the exchange and correlated two-meson potential which is considered as a candidate of the attractive potential.
HYP2006, Mainz,13th Oct 2006
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Parametrization of the potential
HYP2006, Mainz,13th Oct 2006
Parametrization as and exchange model
A B
NN 55.9 3308 158.5 1422
N 47.0 3560 113.2 1466
33.4 4357 70.8 1548
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Comparison with scalar potentials
HYP2006, Mainz,13th Oct 2006
The scalar potential for baryon-baryon interaction is flavor dependent
The scalar potential is more attractive than the N potential