Regge trajectories, detectors, and distributions in the critical ${\rm O}(N)$ model
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909676703055872 |
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| author | Li, Yue-Zhou Simmons-Duffin, David |
| author_facet | Li, Yue-Zhou Simmons-Duffin, David |
| contents | We explore light-ray operators in the critical O$(N)$ model in the large-$N$ limit, focusing on leading-twist and leading ``horizontal" trajectories. We distinguish between light-ray operators in two conformal frames: detector operators, which characterize event shapes of final states, and distribution operators, which probe initial-state distributions. In particular, we identify parton distribution functions (PDFs) and collinear functions as matrix elements of appropriate distribution operators. We renormalize some simple detector operators at leading order in $1/N$, allowing us to extract the Regge intercept and the anomalous spin of the leading horizontal trajectory. We furthermore renormalize distribution versions of these operators, obtaining the leading-twist splitting function and a BFKL-type kernel, which match results from the detector frame. Finally, we show how these results can be read off from OPE data encoded in the Bethe-Salpeter resummation of conformal four-point functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06419 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regge trajectories, detectors, and distributions in the critical ${\rm O}(N)$ model Li, Yue-Zhou Simmons-Duffin, David High Energy Physics - Theory High Energy Physics - Phenomenology We explore light-ray operators in the critical O$(N)$ model in the large-$N$ limit, focusing on leading-twist and leading ``horizontal" trajectories. We distinguish between light-ray operators in two conformal frames: detector operators, which characterize event shapes of final states, and distribution operators, which probe initial-state distributions. In particular, we identify parton distribution functions (PDFs) and collinear functions as matrix elements of appropriate distribution operators. We renormalize some simple detector operators at leading order in $1/N$, allowing us to extract the Regge intercept and the anomalous spin of the leading horizontal trajectory. We furthermore renormalize distribution versions of these operators, obtaining the leading-twist splitting function and a BFKL-type kernel, which match results from the detector frame. Finally, we show how these results can be read off from OPE data encoded in the Bethe-Salpeter resummation of conformal four-point functions. |
| title | Regge trajectories, detectors, and distributions in the critical ${\rm O}(N)$ model |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2506.06419 |