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Scattering amplitudes for all masses and spins

Arkani-Hamed, Nima and Huang, Tzu-Chen and Huang, Yu-tin (2021) Scattering amplitudes for all masses and spins. Journal of High Energy Physics, 2021 (11). Art. No. 70. ISSN 1029-8479. doi:10.1007/jhep11(2021)070.

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We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an extra SU(2) little group index for massive particles, with the amplitudes for spin S particles transforming as symmetric rank 2S tensors. We systematically characterise all possible three particle amplitudes compatible with Poincare symmetry. Unitarity, in the form of consistent factorization, imposes algebraic conditions that can be used to construct all possible four-particle tree amplitudes. This also gives us a convenient basis in which to expand all possible four-particle amplitudes in terms of what can be called “spinning polynomials”. Many general results of quantum field theory follow the analysis of four-particle scattering, ranging from the set of all possible consistent theories for massless particles, to spin-statistics, and the Weinberg-Witten theorem. We also find a transparent understanding for why massive particles of sufficiently high spin cannot be “elementary”. The Higgs and Super-Higgs mechanisms are naturally discovered as an infrared unification of many disparate helicity amplitudes into a smaller number of massive amplitudes, with a simple understanding for why this can’t be extended to Higgsing for gravitons. We illustrate a number of applications of the formalism at one-loop, giving few-line computations of the electron (g − 2) as well as the beta function and rational terms in QCD. “Off-shell” observables like correlation functions and form-factors can be thought of as scattering amplitudes with external “probe” particles of general mass and spin, so all these objects — amplitudes, form factors and correlators, can be studied from a common on-shell perspective.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Huang, Tzu-Chen0000-0002-8738-7695
Huang, Yu-tin0000-0002-3554-7765
Additional Information:© 2021 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: July 27, 2021; Revised: October 24, 2021; Accepted: October 29, 2021; Published: November 10, 2021. We are grateful to Zvi Bern, Rutger Boels, Nathaniel Craig, Lance Dixon and David Kosower for interesting discussions and detailed comments on the draft. We also thank Ming-Zhi Chung, Neil Christensen and Alexander Ochirov for comments for the revised version of the draft. We would especially like to thank the referee’s tremendous effort in carefully working through the manuscript, giving us valuable feed backs. The work of NAH is supported by the DOE under grant DOE DE-SC0009988. Y-t Huang is supported by MoST grant 106-2628-M-002-012-MY3. Y-t Huang would like to thank the Institute for Advanced Study for its hospitality during the completion of this work. T.-C. Huang is supported by the Orr Fellowship.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0009988
Ministry of Science and Technology (Taipei)106-2628-M-002-012-MY3
Dominic Orr Graduate FellowshipUNSPECIFIED
Subject Keywords:Scattering Amplitudes, Higher Spin Gravity, Higher Spin Symmetry
Issue or Number:11
Record Number:CaltechAUTHORS:20211221-766754300
Persistent URL:
Official Citation:Arkani-Hamed, N., Huang, TC. & Huang, Yt. Scattering amplitudes for all masses and spins. J. High Energ. Phys. 2021, 70 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112606
Deposited By: Tony Diaz
Deposited On:21 Dec 2021 20:40
Last Modified:21 Dec 2021 20:40

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