Bjorken and threshold asymptotics of a space-like structure function in the 2D $U(N)$ Gross-Neveu model
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913973574565888 |
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| author | Liu, Yizhuang |
| author_facet | Liu, Yizhuang |
| contents | In this work, we investigate a coordinate space structure function ${\cal E}(z^2m^2,λ)$ 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 $0<z^2<\infty$ and any $ λ\in iR_{\ge 0}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_06787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bjorken and threshold asymptotics of a space-like structure function in the 2D $U(N)$ Gross-Neveu model Liu, Yizhuang High Energy Physics - Theory High Energy Physics - Phenomenology In this work, we investigate a coordinate space structure function ${\cal E}(z^2m^2,λ)$ 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 $0<z^2<\infty$ and any $ λ\in iR_{\ge 0}$. |
| title | Bjorken and threshold asymptotics of a space-like structure function in the 2D $U(N)$ Gross-Neveu model |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2403.06787 |