The gluonic operator matrix elements at O(αs2) for DIS heavy flavor production

We calculate the O(αs2) gluonic operator matrix elements for the twist-2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region Q2≫m2, up to the linear terms in the dimensional parameter ε (D=4+ε). These quantities are required for the description of parton distribution functions in the variable flavor number scheme (VFNS). The O(αs2ε) terms contribute at the level of the O(αs3) corrections through renormalization. We also comment on additional terms, which have to be considered in the fixed (FFNV) and variable flavor number scheme, adopting the MS¯ scheme for the running coupling constant.