Fixed-angle softness of the closed-string amplitude
= Fixed-angle softness of the closed-string amplitude
{title2=$\log|A|\sim-2s f(a)$}
For $t\simeq-as$, $u\simeq-(1-a)s$ with $0<a<1$, the smooth high-energy envelope satisfies $\log|A|\simeq-2s[-a\log a-(1-a)\log(1-a)]$. The <Gamma function> asymptotics cancel the leading $s\log s$ terms, leaving exponential suppression. Exact real-axis resonance poles must be excluded or treated by analytic continuation.