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Published April 2023 | Published
Journal Article Open

Detectors in weakly-coupled field theories


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 ϕ⁴ theory in d = 4 − ϵ 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.

Additional Information

© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. We thank Cyuan-Han Chang, Lance Dixon, Nikolay Gromov, Juan Maldacena, Ian Moult, Andy Strominger, Sasha Zhiboedov, and especially Shota Komatsu for valuable discussions. We additionally thank the organizers and participants of the workshops "Analytic approaches to the bootstrap" in the Azores in 2018, and Bootstrap 2019 at the Perimeter Institute, where this work was initiated. PK and DSD also thank the organizers and participants of the 2019 conference "From Scattering Amplitudes to the Conformal Bootstrap" at the Aspen Center for Physics (supported by National Science Foundation grant PHY1607611). DSD is supported by Simons Foundation grant 488657 (Simons Collaboration on the Nonperturbative Bootstrap) and a DOE Early Career Award under grant No. DESC0019085. PK was supported by DOE grant No. DE-SC0009988, the Adler Family Fund, as well as the Corning Glass Works Foundation Fellowship Fund at the Institute for Advanced Study. Work of SCH is supported by the Simons Collaboration on the Nonperturbative Bootstrap, the Canada Research Chair program and the Sloan Foundation. The work of MK is supported by funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 787185), and by a Yale Mossman Prize Fellowship in Physics. DM was supported by the DOE under grant No. DE-SC0011632 and by the NSF grant PHY-2014071.

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Published - JHEP04_2023_014.pdf


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August 22, 2023
September 11, 2023