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Scalar and intera ction within a chiral un itary approach HYP2006, Mainz,13 th Oct 2006 Kenji Sasaki E. Oset M. J. Vicente Vacas (Valencia University - IFIC)

Scalar LN and LL interaction within a chiral unitary approach

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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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Page 1: Scalar  LN  and  LL  interaction within a chiral unitary approach

Scalar and interaction within a chiral unitary approach

HYP2006, Mainz,13th Oct 2006

Kenji Sasaki

E. Oset

M. J. Vicente Vacas(Valencia University - IFIC)

Page 2: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 3: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 4: Scalar  LN  and  LL  interaction within a chiral unitary approach

Calculation of correlated two-meson potential

Page 5: Scalar  LN  and  LL  interaction within a chiral unitary approach

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 ).

Page 6: Scalar  LN  and  LL  interaction within a chiral unitary approach

Diagrams of two-meson triangle loop

HYP2006, Mainz,13th Oct 2006

Meson-baryon (Octet) interaction

Meson-baryon (Decuplet) interaction

Page 7: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 8: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 9: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 10: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 11: Scalar  LN  and  LL  interaction within a chiral unitary approach

Calculation of uncorrelated two-meson potential

Page 12: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 13: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 14: Scalar  LN  and  LL  interaction within a chiral unitary approach

Results of scalar N and potential

Page 15: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 16: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 17: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 18: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 19: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 20: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 21: Scalar  LN  and  LL  interaction within a chiral unitary approach

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

Page 22: Scalar  LN  and  LL  interaction within a chiral unitary approach

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