Eur. Phys. J. A (2008) 36: 211-218
https://doi.org/10.1140/epja/i2007-10574-3

Regular Article - Theoretical Physics

The σK coupling in the chiral unitary approach and the isoscalar ¯N , ¯A interaction

Departamento de Fısica Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigación de Paterna, Aptdo. 22085, 46071, Valencia, Spain

Received: 20 December 2007
Accepted: 8 April 2008
Published online: 2 May 2008

Abstract

We evaluate the “σ " exchange contribution to the ¯N → ¯N scattering within a chiral unitary approach. We show that the chiral transition potentials for ππ → K¯ in the t -channel lead to a “σ " contribution that vanishes in the ¯ 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 = 0 ππ → 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 ¯N → ¯N 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.