Bjorken and threshold asymptotics of a space-like structure function in the 2D U(N) Gross-Neveu model

In this work, we investigate a coordinate space structure function epsilon(z(2)m(2), lambda) in the 2D U(N) Gross-Neveu model to the next-to-leading order in the large-N expansion. We analytically perform the twist expansion in the Bjorken limit through double Mellin representations. Hard and non-perturbative scaling functions are naturally generated in their Borel representations with detailed enumerations and explicit expressions provided to all powers. The renormalon cancellation at t = n between the hard functions at powers p and the non-perturbative functions at powers p + n are explicitly verified, and the issue of "scale-dependency" of the perturbative and non-perturbative functions is explained naturally. Simple expressions for the leading power non-perturbative functions are also provided both in the coordinate space and the momentum-fraction space (0 < alpha < 1) with "zero-mode-type" subtractions at alpha = 0 discussed in detail. In addition to the Bjorken limit, we also perform the threshold expansion of the structure function up to the next-to-next-to-leading threshold power exactly and investigate the resurgence relation between threshold and "Regge" asymptotics. We also prove that the twist expansion is absolutely convergent for any 0 < z(2) < infinity and any lambda is an element of iR >= 0.