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Geometric soft theorems

Cheung, Clifford and Helset, Andreas and Parra-Martinez, Julio (2022) Geometric soft theorems. Journal of High Energy Physics, 2022 (4). Art. No. 11. ISSN 1126-6708. doi:10.1007/JHEP04(2022)011.

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We derive a universal soft theorem for every scattering amplitude with at least one massless particle in an arbitrary theory of scalars. Our results follow from the geometry of field space and are valid for any choice of mass spectrum, potential terms, and higher-derivative interactions. For a vanishing potential, the soft limit of every amplitude is equal to the field-space covariant derivative of an amplitude with one fewer particle. Furthermore, the Adler zero and the dilaton soft theorem are special cases of our results. We also discuss more exotic scenarios in which the soft limit is non-trivial but still universal. Last but not least, we derive new theorems for multiple-soft limits which directly probe the field-space curvature, as well as on-shell recursion relations applicable to two-derivative scalar field theories exhibiting no symmetries whatsoever.

Item Type:Article
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URLURL TypeDescription Paper
Cheung, Clifford0000-0002-9983-9425
Helset, Andreas0000-0002-5904-3748
Parra-Martinez, Julio0000-0003-0178-1569
Additional Information:© 2022 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. Received 15 November 2021; Revised 23 February 2022; Accepted 11 March 2022; Published 04 April 2022. We are grateful to Lance Dixon, Maria Derda, Aneesh Manohar, and Ira Rothstein for useful discussions and comments on the paper. We also thank Maria Derda, Elizabeth Jenkins, Aneesh Manohar, and Michael Trott for collaboration on related projects. C.C., A.H., and J.P.-M. are supported by the DOE under grant no. DE-SC0011632 and by the Walter Burke Institute for Theoretical Physics.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Subject Keywords:Effective Field Theories; Scattering Amplitudes; Differential and Algebraic Geometry; Sigma Models
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Other Numbering System NameOther Numbering System ID
Issue or Number:4
Record Number:CaltechAUTHORS:20211206-190624588
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Official Citation:Cheung, C., Helset, A. & Parra-Martinez, J. Geometric soft theorems. J. High Energ. Phys. 2022, 11 (2022).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112232
Deposited By: Joy Painter
Deposited On:07 Dec 2021 17:45
Last Modified:06 Apr 2022 18:36

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