Five-point Type IIB string amplitudes at one loop

A bstract Massless type IIB superstring amplitudes are organized according to the number of external states and their U(1) charge under the R-symmetry of type IIB supergravity. In this work, we analyze the low-energy expansion of one-loop five-point amplitudes in all charge sectors, focusing on the representative processes involving five gravitons and four gravitons with one dilaton. We compute the one-loop contributions to the moduli-dependent couplings in the type IIB effective action up to the D 12 R 5 and D 14 ϕR 4 interactions. The results are consistent with S -duality constraints in every charge sector and exhibit rich arithmetic structure, including single-valued multiple zeta values, affine linear combinations of logarithmic derivatives of the Riemann zeta function at odd integers, and a new constant of currently unknown nature.