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<p>We explore light-ray operators in the critical O(<i>N</i>) model in the large-<i>N</i> 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/<i>N</i>, 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.</p>

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Regge trajectories, detectors, and distributions in the critical O(N) model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月13日

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  • Yue-Zhou Li,
  • David Simmons-Duffin

摘要

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.