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 Pz 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 Pz|1 − y| and a pair of heavy-light Sudakov form factors at scale Pz. 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.

Overview of hadron structure from lattice QCD

“…The threshold resummation as investigated in Ref. [102] could enhance the accuracy of the lattice calculation of parton distributions at large-x region. Similarly, the SDF in coordinate space also contains the similar large logarithms and has been investigated in Ref.…”