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Scalar LN and LL interaction within a chiral unitary approach. Kenji Sasaki E. Oset M. J. Vicente Vacas ( Valencia University - IFIC ). HYP2006, Mainz,13 th Oct 2006. Introduction. Using chiral unitary approach, the s meson is dynamically generated as the meson-meson resonance. - PowerPoint PPT Presentation
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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)
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
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
Calculation of correlated two-meson potential
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 ).
Diagrams of two-meson triangle loop
HYP2006, Mainz,13th Oct 2006
Meson-baryon (Octet) interaction
Meson-baryon (Decuplet) interaction
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
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
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
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
Calculation of uncorrelated two-meson potential
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
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
Results of scalar N and potential
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
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
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
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
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
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
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
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