Scalar LN and LL interaction within a chiral unitary approach

1. Scalar LN and LL interaction within a chiral unitary approach Kenji Sasaki E. Oset M. J. Vicente Vacas (Valencia University - IFIC) HYP2006, Mainz,13th Oct 2006

2. Introduction • Using chiral unitary approach, the s 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 “s” 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 • The scalar-isoscalar potential plays an important role in the nucleon-nucleon interaction providing an intermediate range attraction in all channels. • In terms of the OBE, the intermediate attraction is brought by “s”-exchange potential, but the nature of this particle has been a source of controversy. What will be happen in LN and LL interaction? HYP2006, Mainz,13th Oct 2006

3. Scalar baryon-baryon potential w B1 B2 B1 B2 s p, K B1 p, K B2 p, K B1 B2 B2 B1 B2 B1 Same physics in different formalism (dispersion relation,) done by the Julich group J Haidenbauer and U G Meissner Phys Rev C72 (2005) 044005 One-meson exchange Uncorrelated Correlated HYP2006, Mainz,13th Oct 2006

4. Calculation of correlated two-meson potential

5. Correlated two-meson potential B2 B1 B2 B1 T-matrix of meson-meson scattering It reproduces the meson-meson phase shift up to 1.2GeV quite well. calculated by the chiral unitary method. Cancellation mechanism for off-shell part of meson-meson amplitude • (E Oset, H Toki, M Mizobe, and T T Takahashi PTP103 (2000) 351 ). We define the correlated two-meson exchange potential as Triangle scalar loop contribution HYP2006, Mainz,13th Oct 2006

6. Diagrams of two-meson triangle loop Meson-baryon (Octet) interaction Meson-baryon (Decuplet) interaction HYP2006, Mainz,13th Oct 2006

7. Triangle scalar loop contribution 8 M = M m = m p N M = M m = m N K 6 ) q ( D 4 2 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 q [ M e V ] The contribution of the heavy meson loop is suppressed in the small momentum region. HYP2006, Mainz,13th Oct 2006

8. Two meson amplitude in scalar channel p, K p, K Chiral 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

9. 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) 438 J A Oller E Oset and J R Pelaez Phys Rev D59 (1999) 074001 HYP2006, Mainz,13th Oct 2006

10. Correlated two meson potential 2 . 5 - 5 ´ ( 1 0 ) C o r 2 ) 1 . 5 q ( T 1 0 . 5 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 q [ M e V ] HYP2006, Mainz,13th Oct 2006

11. Calculation of uncorrelated two-meson potential

12. Uncorrelated two-meson diagrams Set of diagrams for LN channel Ladder type diagram Cross type diagram Set of diagrams for LL channel HYP2006, Mainz,13th Oct 2006

13. Uncorrelated two meson potential 0 - 2 - 4 L a d d e r t y p e p o t e n t i a l - 6 C r o s s t y p e p o t e n t i a l - 8 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 q [ M e V ] The ladder type (direct) potential is much stronger than the cross type potential HYP2006, Mainz,13th Oct 2006

14. Results of scalar LN and LL potential

15. - 5 - 5 ´ ´ ( 1 0 ) ( 1 0 ) 1 5 1 5 C o r C o r U n C o r U n C o r 1 0 1 0 O m e g a O m e g a T o t a l T o t a l ] ] 5 5 2 2 - - V V e e M M 0 0 [ [ ) ) q q ( ( V V - 5 - 5 - 1 0 - 1 0 - 1 5 - 1 5 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 q [ M e V ] q [ M e V ] Scalar LN 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. HYP2006, Mainz,13th Oct 2006

16. Scalar LN potential in configuration space 1 0 0 1 0 0 C o r C o r U n C o r U n C o r O m e g a O m e g a 5 0 5 0 T o t a l T o t a l ] ] V V e e M M [ [ 0 0 ) ) r r ( ( V V - 5 0 - 5 0 - 1 0 0 - 1 0 0 0 . 5 1 1 . 5 2 2 . 5 3 0 . 5 1 1 . 5 2 2 . 5 3 r [ f m ] r [ f m ] The attraction is produced by both the corr. and uncor. two-meson contribution. The short range repulsion is produced by the correlated two-meson contribution. The two-kaon contribution is very small comparing with two-pion contribution. HYP2006, Mainz,13th Oct 2006

17. Scalar LL potential in momentum space The similar shape of potentials are produced The LL potential is largely enhanced by the two-kaon contribution HYP2006, Mainz,13th Oct 2006

18. LL potential in configuration space Short range repulsion in total potential is smaller than the LN case The two-kaon contribution is relatively stronger than the LN case HYP2006, Mainz,13th Oct 2006

19. The k exchange potential The total k exchange will be attractive in our calculation, but it is very weak. The repulsive potential comes from the correlated meson diagrams HYP2006, Mainz,13th Oct 2006

20. Summary and conclusion • We calculate the scalar-isoscalar LN and LL 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 s-exchange. • Two-kaon exchange contribution is quite small comparing with two-pion contribution in LN channel, on the other hand, it has a large contribution in LL channel. • The short range repulsive potential is generated by both the w exchange and correlated two-meson potential which is considered as a candidate of the attractive s potential. HYP2006, Mainz,13th Oct 2006

21. Parametrization of the potential Parametrization as s and w exchange model HYP2006, Mainz,13th Oct 2006

22. Comparison with scalar potentials The scalar potential for baryon-baryon interaction is flavor dependent The scalar LL potential is more attractive than the LN potential HYP2006, Mainz,13th Oct 2006