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

TL;DR

This paper provides a high-precision three-loop calculation of matching coefficients linking parton distribution functions with lattice QCD correlators, reducing uncertainties and enabling extraction of the three-loop splitting function, with potential for four-loop advancements.

Contribution

It presents the first complete three-loop calculation of matching coefficients and extracts the three-loop splitting function, improving theoretical precision in QCD calculations.

Findings

Reduction in theoretical uncertainties at three-loop order

Extraction of the three-loop unpolarized flavor non-singlet splitting function

Potential to extend calculations to four-loop order

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.