The structure of n-point one-loop open superstring amplitudes

In this article we investigate one-loop amplitudes in maximally supersymmetric superstring theory. The non-anomalous part of the worldsheet integrand is presented for any number of massless open-string states. The polarization dependence is organized into the same BRST-invariant kinematic combinations which also govern the leading string correction to tree-level amplitudes. The dimensions of the bases for both the kinematics and the associated worldsheet integrals is found to be the unsigned Stirling number S₃ⁿ⁻¹ of first kind. We explain why the same combinatorial structures govern on the one hand finite one-loop amplitudes of equal helicity states in pure Yang-Mills theory and on the other hand the color tensors at order α′2 of the color-dressed tree amplitude.