Linear Rising Trajectories in the Time-Delay Analysis of the Scattering Amplitude

Abstract

It is explicitly shown that the integration parameter in the background Regge integral can be understood as a time-delay variable, its average value being the time delay and distortion caused on a wave packet by a scatterer, as seen in the Breit system of coordinates. By means of the usual exponential Fourier transform, another time-delay variable is defined with a similar meaning for the scattering process as seen in the laboratory system of coordinates. The average over the energy of the scattering amplitude is related to a cutoff in the time-delay variables in both cases. A smooth energy variation of the scattering amplitudes corresponds to a small range of variation of the time-delay variable in the transformed amplitude. A Fourier analysis of the Veneziano-model amplitude results in a simple periodic structure in the time-delay variable. A parametrization of the scattering amplitudes in the time-delay representation is proposed, valid at high and intermediate energies. It is pointed out that the non-spin-flip pion-nucleon scattering amplitudes are consistent with such a parametrization. An interpretation of models with linearly rising trajectories in terms of multiscattering processes seems natural in the time-delay representation.