Parton distribution functions (PDFs) are a cornerstone of theoretical predictions for high-energy proton collisions. Their precise determination is essential for fully exploiting the LHC's potential as a precision machine, particularly in view of its high-luminosity upgrade. Although PDFs are intrinsically nonperturbative, their scale evolution is governed by DGLAP splitting functions, which can be computed in perturbative QCD.
In this talk, I present the first complete calculation of the four-loop non-singlet splitting functions, which are required for the consistent inclusion of N3LO QCD corrections in PDF evolution. The exact analytic results across the full range of momentum fractions allow us to study their large- and small-x limits, assess the accuracy of existing approximations, and obtain previously unknown analytic expressions for several anomalous dimensions of broader relevance in perturbative QCD.
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