Abstract
We present a next-to-next-to-leading order (NNLO) realization of a general quark mass scheme (S-ACOT-$\ensuremath{\chi}$) in deep inelastic scattering and explore the impact of NNLO terms on heavy-quark structure functions ${F}_{2,L}^{c}(x,Q)$. An amended QCD factorization theorem for DIS is discussed that validates the S-ACOT-$\ensuremath{\chi}$ scheme to all orders in the QCD coupling strength. As a new feature, kinematical constraints on collinear production of heavy quarks that are crucial near the heavy-quark threshold are included in the amended factorization theorem. An algorithmic procedure is outlined for implementing this scheme at NNLO by using mass-dependent and massless results from literature. At two loops in QCD cut diagrams, the S-ACOT-$\ensuremath{\chi}$ scheme reduces scale dependence of heavy-quark DIS cross sections as compared to the fixed-flavor number scheme.
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