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 $\mathcal{E}(z^2{m}^2,\lambda )$ 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 $0<z^2<\infty$ and any $\lambda \in i{R}_{\ge 0}$.

arXiv commentThis work has 42 pages. Restructured and improved presentation. A new section on the relationship between momentum space and coordinate space expansions added

References in corpus (16)

• Parton Physics on Euclidean Lattice
• Renormalons
• Quasi-PDFs, momentum distributions and pseudo-PDFs
• Large-Momentum Effective Theory
• Anomalous dimensions of high-spin operators beyond the leading order
• Hyperasymptotics and quark-hadron duality violations in QCD
• The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $\sigma$-Model
• Renormalon approach to higher-twist distribution amplitudes and the convergence of the conformal expansion
• IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
• On mass spectrum in 't Hooft's 2D model of mesons
• Overview of lattice calculations of the $x$-dependence of PDFs, GPDs and TMDs
• Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators
• Infrared Renormalons and Power Corrections in Deep-Inelastic Sum Rules
• Large-Nc QCD, Harmonic Sums and the Riemann Zeros
• Structure functions of the 2d O(n) non-linear sigma models
• Structure functions of 2d integrable asymptotically free models

Cited by in corpus (1)

• Renormalon-like factorial enhancements to power expansion/OPE in a super-renormalizable 2D $O(N)$ quartic model