Correlated ππ and KK exchange in the baryon-baryon interaction

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 KK exchange is derived from the amplitudes for the transition of a baryon-antibaryon state (BB′) to a ππ or KK state in the pseudophysical region by applying dispersion theory and unitarity. For the BB′ → ππ, KK 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-KK amplitudes derived likewise from a meson-exchange model, which is in line with the empirical ππ data. The parameters of the BB′ → ππ, KK model, which are related to each other by the assumption of SU(3) symmetry, are determined by the adjustment to the quasiempirical NN → ππ amplitudes in the pseudophysical region. It is found that correlated KK exchange plays an important role in the σ-channel for baryon-baryon states with non-vanishing strangeness. The strength of correlated ππ plus KK 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 KK 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 KK-exchange processes like, e.g. in the Jp = 1−, I = 0 channel (ω, Φ) and πK correlations (K∗), remain to be investigated.