Long-Bin Chen, Wei Wang, and Ruilin Zhu, Next-to-Next-to-Leading Order Calculation of Quasiparton Distribution Functions, Phys. Rev. Lett. 126, 072002, (2021)

In the last few years, there have been significant progresses toward a first principle computation of nucleon parton distribution functions, based on the so-called large momentum effective theory (LaMET), see, a recent review. In this formalism, a quasidistribution is constructed from the lattice calculable matrix element of the hadron state and the relevant light-cone distributions can be derived through a perturbative matching. This provides a powerful tool to calculate all parton observables from the first principle of QCD which can be directly confronted with the experimental measurements. The fixed-order calculation plays an important role in the development of LaMET. It provides not only the explicit expression of the matching coefficients needed for the lattice computation, but also the detailed instances showing how the factorization works. In this paper, we carry out, for the first time,  the next-to-next-to-leading order (NNLO) calculation of quark quasiparton distribution functions (PDFs) in the large momentum effective theory. The nontrivial factorization at this order is established explicitly and the full analytic matching coefficients between the quasidistribution and the light-cone distribution are derived. We demonstrate that the NNLO numerical contributions can improve the behavior of the extracted PDFs sizably. With the unprecedented precision study of nucleon tomography at the planned electron-ion collider, high precision lattice QCD simulations with the NNLO results implemented will enable to test the QCD theory and more precise results on the PDFs of nucleons will be obtained.

Figure: Next-to-next-to-leading order improvement for the extraction of nucleon parton distribution functions (up quark minus down quark) from the lattice computations. Also shown are results from the NNPDF global analysis (R. D. Ball et al., Eur. Phys. J. C 77, 663 (2017)).