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

Abstract

In this work, we investigate a coordinate space structure function E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{E} $$\\end{document}(z2m2, λ) 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 < α < 1) with “zero-mode-type” subtractions at α = 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 < z2 < ∞ and any λ ∈ iR≥0.