Coulomb scattering in the massless Nelson model II. Regularity of ground states

For the massless Nelson model, we provide detailed information about the dependence of the normalized ground states ψP,σ of the fiber single-electron Hamiltonians HP,σ on the total momentum P and the infrared cut-off σ. This information is obtained with the help of the iterative analytic perturbation theory. In particular, we derive bounds of the form ∥∂PiψP,σ∥,∥∂Pi∂PjψP,σ∥≤ c σδΛ0, for some constant c and a function of the maximal admissible coupling constant Λ0→δΛ0 such that limΛ0→0δΛ0 = 0. These results hold both in the infrared-regular and infrared-singular cases. They are exploited in part I of this series to construct the two-electron scattering states in the infrared-regular massless Nelson model (in the absence of an infrared cut-off) along the lines of the Haag-Ruelle scattering theory. They should also be relevant to the problem of scattering of two infraparticles in the infrared-singular Nelson model, whose solution is the goal of this series of papers. Although a part of a larger investigation, the present work is written in a self-contained fashion.