Extracting Parton Distribution Functions from Lattice QCD Calculations

Abstract

Parton distribution functions (PDFs) are nonperturbative quantities describing the relation between a hadron and quarks and gluons within it. We propose to extract PDFs from QCD global analysis of "data" generated by lattice QCD calculations of good "lattice cross sections", which are basically single-hadron matrix elements that are lattice QCD calculable and perturbative QCD factorizable into the PDFs. To demonstrate the existence of good "lattice cross sections", we take quasi-quark distribution introduced by Ji [1] as a case study to show that it could be factorized into the PDFs to all orders in perturbation theory if it can be multiplicatively renormalized. We calculate the factorized coefficients at the next-to-leading order in $α_s$.

Figures (4)

• Figure 1: Ladder expansion of the quasi-quark distribution.
• Figure 2: Process-dependent 2PI kernel with the gauge link along the direction $n_z^\mu$ for quasi-PDFs, and multiplicative UV renormalization factors included.
• Figure 3: Spinor decomposition between two 2PI kernels.
• Figure 4: Next-to-leading order diagrams contribute to the quasi-quark distribution of a quark.