The σK coupling in the chiral unitary approach and the isoscalar anti KN, anti KA interaction

We evaluate the ''σ'' exchange contribution to the anti N→ anti N scattering within a chiral unitary approach. We show that the chiral transition potentials for ππ→ K anti K in the t -channel lead to a ''σ'' contribution that vanishes in the anti K forward direction and, hence, would produce a null ''σ'' exchange contribution to the K- optical potential in nuclear matter in a simple impulse approximation. This is a consequence of the fact that the leading-order chiral Lagrangian gives an I=0ππ→ K anti K amplitude proportional to the squared momentum transfer, q2. This finding poses questions on the meaning or the origin of ''σ'' exchange potentials used in relativistic mean-field approaches to the K- nuclear self-energy. This elementary ''σ'' exchange potential in anti KN→anti KN is compared to the Weinberg-Tomozawa term and is found to be smaller than the present theoretical uncertainties but will be relevant in the future when aiming at fitting increasingly more accurate data. (orig.)