S-channel implications of t-channel unitarity

Abstract

Using t-channel unitarity in the form proposed by Mandelstam, we rederive a scaling law for the partial waves in the s-channel Imƒ l(s) ⋍ √2π e −4sxs −3 β(x) x − 1 2 , x = ls −3 2 , s → ∞ , recently derived by Haan and Mütter. The usefulness of our equations (which, unlike the Haan-Mütter ones, are valid at finite s and not only asymptotically) for phenomenological ππ phase-shift analysis is emphasized.