Analyticity Constraints on Unequal-Mass Regge Formulas

A Regge-pole formula is derived for the elastic scattering of two unequal-mass particles that combines desirable l-plane analytic properties (i.e., a simple pole at l=α in the right-half l plane) and Mandelstam analyticity. It is verified that such a formula possesses the standard asymptotic Regge behavior u^α(s) even in regions where the cosine of the scattering angle of the relevant crossed reaction may be bounded. The simultaneous requirements of l-plane and Mandelstam analyticity enforce important constraints, and the consistency of these constraints is studied. These considerations lead to the appearance of a "background" term proportional asymptotically to u^α(0)-1 which has no analog in the equal-mass problem. We also conclude that a necessary condition for consistency is α(∞)<0.