Regge surfaces and elastic unitarity
Reinhard Oehme · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 1975
General singular Regge surfaces $j=\ensuremath{\alpha}(t)$ of the continued partial-wave amplitude are considered in connection with the requirements of elastic $t$-channel unitarity. In the absence of shielding cuts, threshold branch points of the trajectory function $\ensuremath{\alpha}(t)$ can be used for ordinary and for complex Regge-pole surfaces in order to obtain compliance with the unitarity condition. For complex pole surfaces, there are important constraints concerning the way in which the threshold must appear in $\ensuremath{\alpha}(t)$. Branch-point surfaces are discussed in detail. It is shown that hard branch-point trajectories $\ensuremath{\alpha}(t)$ with $t$-independent character generally cannot be made compatible with elastic unitarity by using threshold branch points of $\ensuremath{\alpha}(t)$. Shielding cuts in the $j$ plane are a natural requirement for these singular surfaces. The notions of "shielding cuts" and "hiding cuts" are defined briefly.