Scattering amplitudes for all masses and spins

Abstract 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,...

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Autores principales:	Nima Arkani-Hamed, Tzu-Chen Huang, Yu-tin Huang
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Scattering Amplitudes Higher Spin Gravity Higher Spin Symmetry Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/9a9ac466fab841ff982fd6b5915ad8f4
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spelling	oai:doaj.org-article:9a9ac466fab841ff982fd6b5915ad8f42021-11-14T12:40:40ZScattering amplitudes for all masses and spins10.1007/JHEP11(2021)0701029-8479https://doaj.org/article/9a9ac466fab841ff982fd6b5915ad8f42021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)070https://doaj.org/toc/1029-8479Abstract 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.Nima Arkani-HamedTzu-Chen HuangYu-tin HuangSpringerOpenarticleScattering AmplitudesHigher Spin GravityHigher Spin SymmetryNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-77 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Scattering Amplitudes Higher Spin Gravity Higher Spin Symmetry Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Scattering Amplitudes Higher Spin Gravity Higher Spin Symmetry Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Nima Arkani-Hamed Tzu-Chen Huang Yu-tin Huang Scattering amplitudes for all masses and spins
description	Abstract 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.
format	article
author	Nima Arkani-Hamed Tzu-Chen Huang Yu-tin Huang
author_facet	Nima Arkani-Hamed Tzu-Chen Huang Yu-tin Huang
author_sort	Nima Arkani-Hamed
title	Scattering amplitudes for all masses and spins
title_short	Scattering amplitudes for all masses and spins
title_full	Scattering amplitudes for all masses and spins
title_fullStr	Scattering amplitudes for all masses and spins
title_full_unstemmed	Scattering amplitudes for all masses and spins
title_sort	scattering amplitudes for all masses and spins
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/9a9ac466fab841ff982fd6b5915ad8f4
work_keys_str_mv	AT nimaarkanihamed scatteringamplitudesforallmassesandspins AT tzuchenhuang scatteringamplitudesforallmassesandspins AT yutinhuang scatteringamplitudesforallmassesandspins
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Scattering amplitudes for all masses and spins

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