Evolution of structure functions at NLO

We develop the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution of the Deep Inelastic Scattering (DIS) structure functions at next-to-leading order (NLO) in αs, formulated directly in terms of the structure functions rather than parton distribution functions (PDFs). We refer to this framework as the physical-basis approach. First, we express the NLO PDFs in terms of the structure functions in momentum space. Substituting these expressions into the DGLAP equations, we derive the evolution equations in the physical basis. We demonstrate that, within this approach, the evolution equations are independent of the choice of factorization scale and scheme. Finally, we discuss the application of the NLO physical basis in calculation of LHC cross sections.