The In-Medium \barK NInteraction within a Chiral Unitary Approach

Abstract

The s-and p-wave contributions to theKN interaction in dense nuclear matter are obtained using a chiral unitary approach. We perform a self-consistent calculation of thē K self-energy including Pauli blocking effects, meson self-energies modified by short-range correlations and baryon binding potentials. We find that the on-shell factorization cannot be applied to evaluate the in-medium corrections to p-wave amplitudes. Furthermore, the Λ and Σ develop a mass shift of -30 MeV at saturation density while the Σ * width increases to 80 MeV. We conclude that no deep and narrowK bound states could be observed.Phenomenology of kaonic atoms shows that theK feels an attractive potential at low densities. This attraction results from the modified s-wave Λ(1405) resonance in the medium 1) due to Pauli blocking effects 2) combined with the self-consistent consideration of theK self-energy 3), 4) and the inclusion of self-energies of the mesons and baryons in the intermediate states. 5) Attraction of the order of -50 MeV at normal nuclear matter density ρ 0 = 0.17 fm −3 is obtained by different approaches, such as unitarizated extensions of chiral theories in coupled-channels. 5)Further studies of higher-partial waves have been performed recently. 6), 7) The p-wave contribution to theKN optical potential has been found to be negligible for atoms. 8) However, heavy-ion collisions can test high-momentum kaons and, therefore, further partial-wave contributions.In this paper we study theK properties in dense matter using a chiral unitary approach which incorporates s-and p-wave contributions to theKN interaction. We show that the on-shell factorization cannot be applied for p-waves in the medium. The self-energy of Λ(1115), Λ(1405), Σ(1195) and Σ * (1385) is also analyzed. 9)TheK self-energy in the nuclear medium and, hence, the spectral density are obtained by incorporating medium modifications to the coupled-channel Bethe-Salpeter equation using, as kernel, tree level chiral contributions. The s-wave contribution is derived from the lowest-order chiral lagrangian that couples the octet of pseudoscalar mesons to the octet of 1/2 + baryons, 10) while the p-wave amplitudes come mainly from the Λ, Σ and Σ * pole terms. 11) For meson-baryon scattering the kernel can be factorized on the mass shell in the loop functions. 10), 12) The loop function is then regularized by means of a cutoff or dimensional regularization. The formal result is * )