TheN/D method and the diffraction picture

Abstract

Elastic spin 0-spin 0 scattering is considered and it is argued that, in order to have a simple connection between the total amplitude and the partial-wave amplitude in the high-energy region, the latter has to satisfy the boundary condition corresponding to the « diffraction picture ». If the amplitude can be written in the conventionalN l (ν)/D l (ν) form, whereN l (ν) has only a left-hand cut andD l (ν) only a right-hand cut, and where there are no arbitrary subtraction constants, it follows that the imaginary part ofD l (ν) behaves likeν−1/2 forν→∞ (apart from possible logarithmic factors).