Parton Distribution Function from the Hadronic Tensor on the Lattice

Understand

The path-integral formulation of the hadronic tensor W_{\mu\nu} of deep inelastic scattering is reviewed.

• It is shown that there are 3 gauge invariant and topologically distinct contributions.
• The separation of the connected sea partons from those of the disconnected sea can be achieved with a combination of the global fit of the parton distribution function (PDF), the semi-inclusive DIS data on the strange PDF and the lattice calculation of the ratio of the strange to $u/d$ momentum fraction in the disconnected insertion.
• We shall discuss numerical issues associated with lattice calculation of the hadronic tensor involving a four-point function, such as large hadron momenta and improved maximum entropy method to obtain the spectral density from the hadronic tensor in Euclidean time.