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 $$ \mathcal{E} $$ (z 2 m 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....
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2024-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP09(2024)093 |
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| author | Yizhuang Liu |
| author_facet | Yizhuang Liu |
| author_sort | Yizhuang Liu |
| collection | DOAJ |
| description | Abstract In this work, we investigate a coordinate space structure function E $$ \mathcal{E} $$ (z 2 m 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 < ∞ and any λ ∈ iR ≥0. |
| format | Article |
| id | doaj-art-2f133cc7bf0142609489a47982f48551 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-2f133cc7bf0142609489a47982f485512025-08-20T02:30:55ZengSpringerOpenJournal of High Energy Physics1029-84792024-09-012024914310.1007/JHEP09(2024)093Bjorken and threshold asymptotics of a space-like structure function in the 2D U(N) Gross-Neveu modelYizhuang Liu0Institute of Theoretical Physics, Jagiellonian UniversityAbstract In this work, we investigate a coordinate space structure function E $$ \mathcal{E} $$ (z 2 m 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 < ∞ and any λ ∈ iR ≥0.https://doi.org/10.1007/JHEP09(2024)0931/N ExpansionField Theories in Lower DimensionsLarge-Order Behaviour of Perturbation TheoryRenormalonsNonperturbative Effects |
| spellingShingle | Yizhuang Liu Bjorken and threshold asymptotics of a space-like structure function in the 2D U(N) Gross-Neveu model Journal of High Energy Physics 1/N Expansion Field Theories in Lower Dimensions Large-Order Behaviour of Perturbation Theory Renormalons Nonperturbative Effects |
| title | Bjorken and threshold asymptotics of a space-like structure function in the 2D U(N) Gross-Neveu model |
| title_full | Bjorken and threshold asymptotics of a space-like structure function in the 2D U(N) Gross-Neveu model |
| title_fullStr | Bjorken and threshold asymptotics of a space-like structure function in the 2D U(N) Gross-Neveu model |
| title_full_unstemmed | Bjorken and threshold asymptotics of a space-like structure function in the 2D U(N) Gross-Neveu model |
| title_short | Bjorken and threshold asymptotics of a space-like structure function in the 2D U(N) Gross-Neveu model |
| title_sort | bjorken and threshold asymptotics of a space like structure function in the 2d u n gross neveu model |
| topic | 1/N Expansion Field Theories in Lower Dimensions Large-Order Behaviour of Perturbation Theory Renormalons Nonperturbative Effects |
| url | https://doi.org/10.1007/JHEP09(2024)093 |
| work_keys_str_mv | AT yizhuangliu bjorkenandthresholdasymptoticsofaspacelikestructurefunctioninthe2dungrossneveumodel |