  We compute the imaginary parts of genus-one string scattering amplitudes.
Following Witten's $i\varepsilon$ prescription for the integration contour on
the moduli space of worldsheets, we give a general algorithm for computing
unitarity cuts of the annulus, M\"obius strip, and torus topologies exactly in
$\alpha'$. With the help of tropical analysis, we show how the intricate
pattern of thresholds (normal and anomalous) opening up arises from the
worldsheet computation. The result is a manifestly-convergent representation of
the imaginary parts of amplitudes, which has the analytic form expected from
Cutkosky rules in field theory, but bypasses the need for performing laborious
sums over the intermediate states. We use this representation to study various
physical aspects of string amplitudes, including their behavior in the $(s,t)$
plane, exponential suppression, decay widths of massive strings, total cross
section, and low-energy expansions. We find that planar annulus amplitudes
exhibit a version of low-spin dominance: at any finite energy, only a finite
number of low partial-wave spins give an appreciable contribution to the
imaginary part.
