Finite sum of gluon ladders and high energy cross sections

Abstract

A model for the Pomeron at $t=0$ is suggested. It is based on the idea of a finite sum of ladder diagrams in QCD. Accordingly, the number of s-channel gluon rungs and correspondingly the powers of logarithms in the forward scattering amplitude depends on the phase space (energy) available, i.e., as energy increases, progressively new prongs with additional gluon rungs in the s-channel open. Explicit expressions for the total cross section involving two and three rungs or, alternatively, three and four prongs [with ${\mathrm{ln}}^{2}(s)$ and ${\mathrm{ln}}^{3}(s)$ as highest terms, respectively] are fitted to the proton-proton and proton-antiproton total cross section data in the accelerator region. Both QCD calculation and fits to the data indicate fast convergence of the series. In the fit, two terms (a constant and a logarithmically rising one) almost saturate the whole series, the ${\mathrm{ln}}^{2}(s)$ term being small and the next one, ${\mathrm{ln}}^{3}(s),$ negligible. Theoretical predictions for the photon-photon total cross section are also given.