Isospin quantum distances in hadron-hadron scattering

In the last time there is a revival of interest in the idea of introducing geometrical structures on Hilbert space of quantum states. The geometric phase and geometric distance functions are intimately related via length of the curve for any parametric evolution of the quantum system. On the other hand, the optimal states introduced by us and as solution of the minimum norm problem, are used to define an optimal state distance in reproducing kernel Hilbert spaces of the scattering amplitudes. Then, the quantum distance of any scattering state to the optimal states, as a measurable quantity, expressed in terms of the reproducing kernels and differential cross sections, is introduced. In an earlier paper, the quantum distances between two isospin (U-spin, V-spin, etc) channels, in the Hilbert spaces of the hadron-hadron scattering amplitudes, are investigated for the first time. These isospin quantum distances as well as their isospin bounds are expressed in terms of the channel cross sections and polarization parameters. The essential features of the isospin quantum distances for the πN-scattering are calculated for all (s,t,u)-channels by using the available phase shift analyses. (authors)