Correlated ππ and [formula omitted] exchange in the baryon-baryon interaction

Abstract

The exchange of two correlated pions or kaons provides the main part of the intermediate-range interaction between two baryons. Here, a dynamical model for correlated two-pion and two-kaon exchange in the baryon-baryon interaction is presented, both in the scalar-isoscalar (σ) and the vector-isovector (ϱ) channel. The contribution of correlated ππ and K K exchange is derived from the amplitudes for the transition of a baryon-antibaryon state ( B B′ ) to a ππ or K K state in the pseudophysical region by applying dispersion theory and unitarity. For the B B′ → ππ , K K amplitudes a microscopic model is constructed, which is based on the hadron-exchange picture. The Born terms include contributions from baryon exchange as well as ϱ-pole diagrams. The correlations between the two pseudoscalar mesons are taken into account by means of ππ-K K amplitudes derived likewise from a meson-exchange model, which is in line with the empirical ππ data. The parameters of the B B′ → ππ , K K model, which are related to each other by the assumption of SU(3) symmetry, are determined by the adjustment to the quasiempirical N N → ππ amplitudes in the pseudophysical region. It is found that correlated K K exchange plays an important role in the σ-channel for baryon-baryon states with non-vanishing strangeness. The strength of correlated ππ plus K K exchange in the σ-channel decreases with the strangeness of the baryon-baryon system becoming more negative. Due to the admixture of baryon-exchange processes to the SU(3)-symmetric ϱ-pole contributions the results for correlated ππ exchange in the vector-isovector channel deviate from what is expected in the naive SU(3) picture for genuine ϱ-exchange. In present models of the hyperon-nucleon interaction contributions of correlated ππ and K K exchange are parametrized for simplicity by single σ- and ϱ-exchange. Shortcomings of this effective description, e.g. the missing long-range contributions, are pointed out by comparison with the dispersion-theoretic results. It is pointed out that further correlations, namely other K K- exchange processes like, e.g. in the J p = 1 −, I = 0 channel (ω, Φ) and πK correlations ( K ∗ ), remain to be investigated.