Lattice calculation of hadronic tensor of the nucleon

We report an attempt to calculate the deep inelastic scattering structure functions from the hadronic tensor calculated on the lattice. We used the Backus-Gilbert reconstruction method to address the inverse Laplace transformation for the analytic continuation from the Euclidean to the Minkowski space. 1 Hadronic tensor on the lattice There has been a lot of interest and developments in calculating the structure functions and parton distribution functions on the lattice in recent years [1]. The Euclidean hadronic tensor has been formulated in the path-integral formalism [2–4]. The hadronic tensor in deep inelastic scattering, from which the parton distribution functions are obtained through the factorization theorem, can be calculated from its Euclidean counterpart via an inverse Laplace transform [1, 2, 4]. It has been revealed that, in addition to the valence partons, there are two types of sea partons – connected sea (CS) and disconnected sea (DS) in three topologically distinct path-integral diagrams. The extended evolution equations to accommodate both the connected and disconnected sea partons are derived [5]. It is essential to have separately evolved CS and DS partons so that comparison with lattice calculations of unpolarized and polarized moments of PDF can be made. Only with the extended evolution equations will the CS and DS partons remain separated at different Q2 to facilitate global fitting of PDF with separated CS and DS partons. The definition of hadronic tensor in the Minkowski space is Wμν(q, ν) = 1 4π ∫ d4zeiq·z〈p|J† μ(z)Jν(0)|p〉spin ave.