Heavy quark fragmentation in deep inelastic scattering

We perform an analysis of the semi-inclusive production of charm $(D$ mesons) in neutral current (NC) and charged current (CC) deep inelastic scattering (DIS) at full $\mathcal{O}\left({\alpha }_s^1\right).\mathrm{}$ Our calculation is based on the heavy quark scheme developed by Aivazis, Collins, Olness, and Tung where we include an $\mathcal{O}\left({\alpha }_s^1\right)$ calculation of quark scattering contributions for general masses and couplings. We review the relevant massive formulas and subtraction terms and discuss their massless limits. We show how the charm fragmentation function can be measured in CC DIS and we investigate whether the charm production dynamics may be tested in NC DIS. We also discuss finite initial state quark mass effects in CC and NC DIS.