Effects of threshold resummation for large-x PDF in large momentum effective theory

Abstract

Abstract Parton distribution functions (PDFs) at large x are challenging to extract from experimental data, yet they are essential for understanding hadron structure and searching for new physics beyond the Standard Model. Within the framework of the large momentum P z expansion of lattice quasi-PDFs, we investigate large x PDFs, where the matching coefficient is factorized into the hard kernel, related to the active quark momentum xP z, and the threshold soft function, associated with the spectator momentum (1 − x)P z. The renormalization group equation of the soft function enables the resummation of the threshold double logarithms α k ln2k (1 − x), which is crucial for a reliable and controllable calculation of large x PDFs. Our analysis with pion valence PDFs indicates that perturbative matching breaks down when the spectator momentum (1 − x)P z approaches ΛQCD, but remains valid when both xP z and (1 − x)P z are much larger than ΛQCD. Additionally, we incorporate leading renormalon resummation within the threshold framework, demonstrating good perturbative convergence in the region where both spectator and active quark momenta are perturbative scales.

Keywords

• Factorization
• Renormalization Group
• Lattice QCD
• Parton Distributions
• Resummation