Lattice-QCD Computable Quark Correlation Functions at Three-Loop Order and Extraction of Splitting Functions.

Area of Science:

• High Energy Physics
• Quantum Chromodynamics
• Computational Physics

Background:

• Parton distribution functions (PDFs) describe particle momentum inside hadrons.
• Lattice Quantum Chromodynamics (QCD) provides a non-perturbative approach to QCD.
• Matching coefficients are crucial for connecting theoretical calculations with experimental observables.

Purpose of the Study:

• To perform the first complete next-to-next-to-next-to-leading-order (N3LO) calculation of matching coefficients.
• To reduce theoretical uncertainties in the analysis of unpolarized flavor nonsinglet PDFs.
• To extract the three-loop unpolarized flavor nonsinglet splitting function.

Main Methods:

• Calculation of matching coefficients at N3LO.
• Utilizing lattice QCD computable correlation functions.
• Extraction of splitting functions from the calculated coefficients.

Main Results:

• The first complete N3LO calculation of matching coefficients for unpolarized flavor nonsinglet PDFs.
• A significant reduction in theoretical uncertainties compared to lower-order calculations.
• Extraction of the three-loop splitting function, consistent with existing state-of-the-art results.

Conclusions:

• The N3LO calculation provides a more precise link between PDFs and lattice QCD.
• The developed method simplifies the extraction of splitting functions.
• This work paves the way for future four-loop order calculations of splitting functions.