Dynamical model for correlated two-pion exchange in the pion-nucleon interaction

Abstract

A microscopic model for the N N → ππ process is presented in the meson exchange framework, which in the pseudophysical region agrees with available quasiempirical information. The scalar (σ) and vector (ρ) piece of correlated two-pion exchange in the pion-nucleon interaction is then derived via dispersion integrals over the unitarity cut. Inherent ambiguities in the method and implications for the description of pion-nucleon scattering data are discussed.

Jülich hyperon-nucleon model revisited

“…The correlations between the two mesons have been taken into account by means of ππ − KK amplitudes, determined in the field theoretical framework of Refs. [16][17][18], which provide an excellent description of empirical ππ data up to 1.3 GeV. With the help of unitarity and dispersion-theoretical methods, the baryonbaryon amplitudes for correlated ππ and KK exchange in the J P = 0 + (σ ) and J P = 1 − (ρ) t-channels have then been determined.…”

“…For details on the model and a comparision of the resulting ππ phase shifts with experimental values we refer the reader to Refs. [17,18].…”

“…[14], but was extended in a recent paper [15] by the Jülich group so that now a full and consistent microscopic derivation of correlated ππ exchange in various baryon-baryon (BB ) channels with strangeness S = 0, −1, and −2 is available. The starting point was a field theoretical model for both the NN → ππ Born amplitudes and the ππ and KK elastic scattering [16][17][18]. Thus, the KK channel is treated on an equal footing with the ππ channel in order to reliably determine the influence of KK correlations in the relevant t-channels.…”

Role of correlated two-pion exchange in K+N scattering

“…9 of Ref. [7]). The only difference is that there all results scale by a factor of (roughly) 3, in distinct disagreement with the SU (3) value of 2 for the g ππρ /g KKρ ratio.…”

“…Here V NN ,aa is the transition interaction from NN to aa = ππ, KK, T aa,KK are transition amplitudes from ππ and KK to KK, and g aa is the free two-particle Green's function for the as in a recent study of πN scattering [7], we use a model with essentially the same physical input, which alternatively uses the BbS scheme. The description of the data turns out to be as successful as in Ref.…”