Detectors in weakly-coupled field theories

TL;DR

This paper studies asymptotic detector operators in weakly-coupled field theories, focusing on their renormalization, anomalous dimensions, and contributions to correlation functions, with detailed calculations in $\,\phi^4$ theory.

Contribution

It introduces a framework for analyzing detector operators at null infinity, including their renormalization and anomalous dimensions, with explicit results at the Wilson-Fisher fixed point.

Findings

Renormalization of detector operators in perturbation theory.

Explicit two-loop expression for Pomeron light-ray operator.

Prediction of Regge intercept at five loops.

Abstract

We initiate a study of asymptotic detector operators in weakly-coupled field theories. These operators describe measurements that can be performed at future null infinity in a collider experiment. In a conformal theory they can be identified with light-ray operators, and thus have a direct relation to the spectrum of the theory. After a general discussion of the underlying physical picture, we show how infrared divergences of general detector operators can be renormalized in perturbation theory, and how they give rise to detector anomalous dimensions. We discuss in detail how this renormalization can be performed at the intersections of the Regge trajectories where non-trivial mixing occurs, which is related to the poles in anomalous dimensions at special values of spin. Finally, we discuss novel horizontal trajectories in scalar theories and show how they contribute to correlation functions. Our calculations are done in the example of $\phi^4$ theory in $d=4-\epsilon$ dimensions, but the methods are applicable more broadly. At the Wilson-Fisher fixed point our results include an explicit expression for the Pomeron light-ray operator at two loops, as well as a prediction for the value of the Regge intercept at five loops.