Non-analytic terms of string amplitudes from partial waves

We describe a general formalism based on the partial-wave decomposition to compute the iterative $s$-channel discontinuity of four-point amplitudes at any loop order. As an application, we focus on the low-energy expansions of type I and II superstring amplitudes. Besides providing new results for their leading and sub-leading logarithmic contributions beyond genus one, our approach elucidates the general structure of non-analytic threshold terms. In the case of open strings, the use of orthogonal colour projectors allows us to efficiently compute all contributions from different worldsheet topologies at a given loop order.