Quark correlation functions at three-loop order and extraction of splitting functions

Abstract

We present the first complete next-to-next-to-next-to-leading-order calculation of the matching coefficients that link unpolarized flavor non-singlet parton distribution functions with lattice QCD computable correlation functions. By using this high-order result, we notice a reduction in theoretical uncertainties compared to relying solely on previously known lower-order matching coefficients. Furthermore, based on this result we have extracted the three-loop unpolarized flavor non-singlet splitting function, which is in agreement with the state-of-the-art result. Due to the simplicity of our method, it has the potential to advance the calculation of splitting functions to the desired four-loop order.