Hadron structure from current-current correlation functions in Lattice QCD

It has been shown that a class of matrix elements of two spatially-separated currents, which are computable directly in Lattice QCD, can be factorized into parton distribution functions with calculable hard coefficients [Phys.Rev.Lett. 120 (2018) no.2, 022003]; in the same manner as the parton distribution functions are extracted from the hadronic cross sections measured in an experiment. We will discuss this most generalized method to obtain parton distribution functions from a Lattice QCD calculation.

We also discuss the direct Lattice QCD calculation of hadronic tensor which can shed light on the understanding of parton physics in the deep inelastic scattering (DIS) region and neutrino-nucleus scatterings in the shallow inelastic scattering (SIS) region. In this talk, we will briefly introduce the framework of calculating hadronic tensor on the lattice and present some preliminary results.