The Mellin moments of the heavy-quark structure functions in deep-inelastic scattering are computed at next-to-leading order in quantum chromodynamics, retaining the full dependence on the heavy-quark mass throughout.
Combining the optical theorem with the operator product expansion, analytic expressions are obtained for the fixed Mellin moments $N = 2$ to $22$ of the structure functions $F_2$ and $F_L$ at next-to-leading order.
These results reproduce the known expressions in the relevant asymptotic limits, in particular for photon virtualities $Q^2$ much larger than the heavy-quark mass squared $m^2$, and agree with existing parametrisations of the next-to-leading-order coefficient functions.
The principal outcome of this work, however, is the computational framework itself, which has been designed to carry directly over to higher orders.
Building on the validated next-to-leading-order framework, work towards the next-to-next-to-leading-order calculation is already underway, with first progress reported here.