On the Regge-cut cancellation in planar amplitudes of the dual unitarisation scheme

Abstract

The problem of the Regge-cut cancellation in equations for planar reggeons is considered by using the j-plane methods in treating the underlying integral equations. It is shown that the kernel should have the zero which cancels the reggeon-loop singularity in order to eliminate the cut in the reggeon-reggeon scattering amplitude besides amplitudes involving external particles. This zero (nonsense zero) implies that the finite size cluster is incompatible with the cut cancellation. Two alternative no-double-counting conditions of the “reggeon bootstrap” (the Oxford-Rutherford model and the Finkelstein-Koplik model) are examined and it is found that the Regge cut cannot be cancelled because of the finite size of the cluster. Substantial modifications of the “reggeon bootstrap” model may be necessary if the Regge cut is to be cancelled.