Abstract:
Summation of all logarithmic contributions of all diagrams of pseudoscalar meson theory
at high energies leads to a new representation for the small-angle scattering amplitude
for hadrons. This representation contains moving poles and fixed singularities in the $j$
plane. If the renormalizations of the coupling constants and the wave functions are finite,
the fixed singularities are fixed square-root branch points. This representation may serve
as a basis for a well-founded phenomenologieal description of high-energy scattering and
as the starting point for a study of the properties of the Regge trajectories. In particular,
it is already clear that it yields the conspiring trajectories $\pi$ and $\pi_C$ and that the residues
of the amplitudes of meson-baryon and baryon-baryon scattering are proportional to $j=\alpha(t)$, i.e., they lead to dips in the angular distributions at $\alpha(t)=0$.