Threshold resummation for computing large-$x$ parton distribution through large-momentum effective theory

Abstract

Parton distribution functions (PDFs) at large $x$ are poorly constrained by high-energy experimental data, but extremely important for probing physics beyond standard model at colliders. We study the calculation of PDFs at large-$x$ through large-momentum $P^z$ expansion of the lattice quasi PDFs. Similar to deep-inelastic scattering, there are two distinct perturbative scales in the threshold limit where the matching coefficient can be factorized into a space-like jet function at scale $P^z|1-y|$ and a pair of heavy-light Sudakov form factors at scale $P^z$. The matching formula allows us to derive a full renormalization group resummation of large threshold logarithms, and the result is consistent with the known calculation to the next-to-next to leading order (NNLO). This paves the way for direct large-$x$ PDFs calculations in lattice QCD. As by-products, we find that the space-like jet function is related to a time-like version calculated previously through analytic continuation, and the heavy-light Sudakov form factor, calculated here to NNLO, is a universal object appearing as well in the large momentum expansion of quasi transverse-momentum-dependent PDFs and quasi wave-function amplitudes.

53 pages, 7 figures

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Cited by in corpus (9)

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• Lattice QCD Calculation of $x$-dependent Meson Distribution Amplitudes at Physical Pion Mass with Threshold Logarithm Resummation
• Quasi Transverse Momentum Dependent Distributions at Next-to-Next-to-Leading order
• Generalized parton distributions from the pseudo-distribution approach on the lattice
• Three-dimensional Imaging of Pion using Lattice QCD: Generalized Parton Distributions
• Resummation for Lattice QCD Calculation of Generalized Parton Distributions at Nonzero Skewness
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Revisiting the time-ordering issue of TMD soft factors: causality, coordinate space analyticity and new equalities