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

Introduction 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 “  ”-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) HYP2006, Mainz,13th Oct 2006 B1B1 B2B2  B1B1 B2B2  B1B1 B2B2  B1B1 B2B2 B1B1 B2B2 B1B1 B2B2

Calculation of correlated two-meson potential

    Correlated two-meson potential We 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. HYP2006, Mainz,13th Oct 2006

Two meson amplitude in scalar channel 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 

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) HYP2006, Mainz,13th Oct 2006

Correlated two meson potential 2.5 Cor T ( q ) q[MeV] (  ) 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 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. HYP2006, Mainz,13th Oct 2006

Scalar  N potential in configuration space 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 NN 

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