The Pomeron from dual models: Beyond the naive geometrical picture

A generalization of the geometrical model of Chou and Yang incorporating energy dependence and analyticity is suggested. It is based on a Pomeron exchange with a trajectory αP(t)=α0-γln(1-βt) suggested by suitably approximating analyticity preserving dual models. Various limits and approximations are discussed and it is shown how, naturally, one is lead to energy dependent form factors. An explicit Born approximation to the Pomeron is constructed, the secondary reggeons are properly added and the eikonalization procedure is carried out. The description of the high energy pp and anti pp data is shown to improve considerably not only when the radii increase with energy but even more so when this increase is different for protons and antiprotons. Taken at face value, our analysis implies that the pp interaction size increases faster than the anti pp one with increasing energy. LHC energies would prove or disprove quite clearly our claim. (orig.)