S-Channel Unitarity in the Pomeron Theory with α_p(0) > 1

Abstract

The integral equation defining the scattering amplitude in the form of the sum of all pomeron graphs contributions is obtained in the theory with ${{\alpha }_{P}}\left( 0 \right)>1$. It is shown that for definite restrictions on the Cardy’s vertex $Goo\left( {{k}^{2}} \right)$ of the pomeron coupling, the solution of this equation in the ξ, b — representation $\xi =In{{\left( {}^{s}\!\!\diagup\!\!{}_{m}\; \right)}^{2}}$ is the simple amplitude $\theta \left( a\xi -b \right)$, with $a=4{{{a}'}_{P}}\bullet\Delta ,\Delta ={{a}_{P}}\left( 0 \right)-1.$. It leads to the Froissart type rising cross sections, and diffraction cone slopes:${{\sigma }^{tot}}\sim B\sim {{\xi }^{2}}.$