General-mass treatment for deep inelastic scattering at NNLO in CTEQ PDF analysis

We present an NNLO realization of the general mass scheme S-ACOT-$\chi$ for the treatment of heavy-flavour production in neutral current deep-inelastic scattering. Practical implementation of the NNLO calculation is illustrated on the example of semi-inclusive structure functions $F_{2c}(x,Q)$ and $F_{Lc}(x,Q)$. In a modern global QCD analysis of parton distribution functions (PDFs), several factors are comparable in magnitude to next-to-next-to-leading order (NNLO) radiative contributions in the QCD coupling strength $\alpha_s$. Among these factors, dependence of QCD cross sections on masses of heavy quarks, $m_c$ and $m_b$, can be significant. Global fits are sensitive to two types of mass effects, kinematical suppression of production of c and b quarks near respective mass thresholds in deep inelastic scattering (DIS), and large radiative contributions to collinear production of $\bar{c} c$ or $\bar{b}b$ pairs at large collider energy. It is therefore natural to evaluate all fitted cross sections in a ``general-mass'' (GM) factorization scheme, which assumes that the number of (nearly) massless quark flavors varies with energy, and at the same time includes dependence on heavy-quark masses in relevant kinematical regions. The S-ACOT-$\chi$ scheme that we present, is motivated by the QCD factorization theorem for DIS with massive quarks and we show it is valid to all orders of $\alpha_s$.