Regge trajectories, detectors, and distributions in the critical ${\rm O}(N)$ model

TL;DR

This paper investigates light-ray operators in the critical O(N) model at large N, identifying their roles in event shape characterization and initial-state distributions, and computes key quantities like Regge intercepts and splitting functions.

Contribution

It introduces a detailed analysis of light-ray operators in the critical O(N) model, connecting detector and distribution operators, and computes their renormalization and related physical quantities.

Findings

Computed Regge intercept and anomalous spin of leading trajectories.

Derived leading-twist splitting function and BFKL kernel.

Connected operator analysis to OPE data via Bethe-Salpeter resummation.

Abstract

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.