High-energy behaviour of diagrams with crossed lines

Research paper by P. Kaschluhn, W. Zoellner

Indexed on: 25 Nov '07Published on: 25 Nov '07Published in: Il Nuovo Cimento (1955-1965)


The analytic behaviour in the angular momentum plane is studied for the series of iterated diagrams with two crossed lines in ϕ3-theory. The corresponding integral equation for the scattering amplitude which is of positive signature on the mass shell is solved in Fredholm form and it is shown that the series expansions are convergent for Rel > − 3/2 in the cut s-plane. Since the kernel of the integral equation is nonseparable the scattering amplitude has an accumulation of Eegge poles atl = −1 in accordance with the Gribov-Pomeranchuk result. In the weak coupling limit the rightmost Eegge poles must tend tol = −1.