A one-dimensional approximation for the pomeron in the dual unitarity scheme

Using a one-dimensional approximation, the pomeron in the dual unitarity scheme is examined analytically in a multiperipheral cluster model. Clusters have negative short range correlations due to the t_min effect. In dual models, the pomeron has a crossing odd part, especially in B$\text{B}$ and BB scattering. By taking all reggeon loops into account, we show explicitly in our approximation that the crossing-odd part has only lower-lying singularities in the j-plane (typically complex poles with $\text{Re}\text{α?0.2}$) whereas the crossing-even part has the leading singularity at j = α_P (we imposed α_P = 1). The dual unitarity scheme leads to a modified version of the f-dominance of the pomeron. We calculate the SU(3) breaking of the pomeron due to the SU(3) breaking among Regge trajectories without additional assumptions on the SU(3) property of the pomeron.