 Fixed-angle softness of an open-string amplitude

At high energy with $x=-t/s\in (0,1)$ fixed, reflection and Stirling formulas for the Gamma function give the displayed exponential envelope, away from real-axis resonance poles or after suitable analytic continuation. It is softer than the power-law fixed-angle behavior of typical point-particle interactions and exposes the finite string length. This limit differs from the fixed-$t$ Regge limit and does not by itself prove finiteness of every loop amplitude.