Quantum field theory and diffraction scattering of~mesons and baryons

V. M. Budnev ; I. F. Ginzburg ; V. G. Serbo

Teoretičeskaâ i matematičeskaâ fizika, Tome 6 (1971) no. 1, pp. 55-70

Résumé

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 $\alpha(t)=0$.