Heavy Quark Production in DIS: Mellin Moments of Coefficient Functions at NNLO

Abstract

Heavy-quark production in deep-inelastic scattering is studied for neutral, charged and scalar currents. Since exact results with full mass dependence are available only up to next-to-leading order, fixed Mellin moments of the massive coefficient functions are computed instead. Harmonic projection of the forward Compton amplitude circumvents all phase-space integrations. The loop integrals encountered are organised into a minimal set of integral families, reduced by integration-by-parts identities, and solved with the method of differential equations in terms of iterated integrals. At next-to-leading order, this yields the first eleven even moments of the vector--vector contribution to the neutral current, together with the axial--axial and axial--vector contributions, whose deviation is traced to the chiral anomaly. The main result is the computation of all three-loop integrals for the neutral and charged currents, together with the first exact determination at next-to-next-to-leading order: the lowest even moment of the neutral current structure functions, in which elliptic structures of the three-loop banana integral appear. These moments provide model-independent constraints on the approximate coefficient functions.