Toward N${}^3$LO CT global PDF analyses: The SACOT-$\chi$ scheme in DIS and DGLAP evolution at partial N${}^3$LO

We discuss three aspects of the ongoing efforts of the CTEQ–TEA group toward global parton distribution function (PDF) analyses beyond NNLO accuracy in QCD. First, we present a realization of the SACOT-$\chi$ general-mass variable flavor number scheme for deep-inelastic scattering (DIS) at the partial next-to-next-to-next-to-leading order (pN${}^3$LO) in QCD. We numerically illustrate how this SACOT-$\chi$ theory prediction captures the dependence of DIS structure functions on masses of heavy quarks with inclusion of the available $O({\alpha }_s^3)$ contributions. Second, we discuss a preliminary pN${}^3$LO CT25 fit that implements such contributions. Third, we extend the Candia algorithm for solving DGLAP evolution equations for unpolarized parton distribution functions (PDFs) in $x$ space to N${}^3$LO in QCD. The algorithm is based on logarithmic expansions of the solution and can be extended to all orders in QCD. An expansion equivalent to the exact DGLAP solution at N${}^3$LO is presented in the non-singlet sector. We show results for approximate N${}^3$LO PDFs evolved using the most recent approximations to the 4-loop splitting functions in QCD.