Heavy-quark production in deep-inelastic scattering -- Mellin moments of structure functions

We compute Mellin moments of the heavy-quark structure functions in deep-inelastic scattering at next-to-leading order in quantum chromodynamics, retaining their full dependence on the heavy-quark mass. Using the optical theorem and the operator product expansion, we derive analytic results for fixed Mellin moments $N = 2$ to $22$ of the structure functions $F_2$ and $F_L$. Our results reproduce the known expressions in the relevant asymptotic limits, in particular for virtualities of the exchanged photon $Q^2$ much larger than the heavy-quark mass squared $m^2$, and are in agreement with existing parametrisations of the next-to-leading-order coefficient functions. The computational set-up developed in this work also provides a direct pathway toward extending these calculations to next-to-next-to-leading order.