Cluster formulation in the dual topological unitarization scheme

Abstract

The work of Chiu, Hossain, and Tow is generalized by incorporating the no-double-counting condition and the ${t}_{min}$ effect in the integral equations for the Reggeon and the Pomeron. The relation between the no-double-counting condition and the average cluster separation is derived, and a test is proposed to determine the correct counting. It is shown that the ${t}_{min}$ effect is quite important in determining the Regge parameters. The model predicts a relation between five physical quantities: the Pomeron intercept (${\ensuremath{\alpha}}_{P}^{0}$) and slope (${\ensuremath{\alpha}}_{P}^{\ensuremath{'}}$), the magnitude ($k$) and the exponential dependence ($b$) of the triple-Regge vertex, and the ratio of Pomeron to Reggeon residues ($c$) at $t=0$. The solutions obtained are well within the range of acceptable values. A reasonable solution is, for example (in GeV units), ${\ensuremath{\alpha}}_{P}^{0}=0.92$, ${\ensuremath{\alpha}}_{P}^{\ensuremath{'}}=0.2$, $b=1.6$, $k=12.9$, and $c=0.91$. It is found that cuts are present in both the Reggeon and the Pomeron amplitudes, and their contributions are small compared to the leading poles.