= Fixed-angle softness of an open-string amplitude
{title2=$\log|A|\sim-\alpha's[-x\log x-(1-x)\log(1-x)]$}
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.
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