Off mass shell dual amplitude with Mandelstam analyticity

Abstract

A model for the $Q^2$-dependent dual amplitude with Mandelstam analyticity (DAMA) is proposed. The modified DAMA (M-DAMA) preserves all the attractive properties of DAMA, such as its pole structure and Regge asymptotics, and leads to a generalized dual amplitude $A(s,t,Q^2)$. This generalized amplitude can be checked in the known kinematical limits, i.e. it should reduce to the ordinary dual amplitude on mass shell, and to the nuclear structure function when $t=0$. In such a way we complete a unified "two-dimensionally dual" picture of strong interaction. By comparing the structure function $F_2$, resulting from M-DAMA, with phenomenological parameterizations, we fix the $Q^2$-dependence in M-DAMA. In all studied regions, i.e. in the large and low $x$ limits as well as in the resonance region, the results of M-DAMA are in qualitative agreement with the experiment.