Scattering amplitudes for all masses and spins

By N. Arkani-Hamed, Tzu-Chen Huang, Yu-tin Huang. Journal of High Energy Physics, 2017

357 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f5f8def625b147f6a7482c16c0119bcc0a2fda76

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Citations in the corpus

The cosmological bootstrap: inflationary correlators from symmetries and singularities (2018, neutral): “This is a In the case of massless particles, the requirement of consistent factorization of four-particle amplitudes is highly restrictive, and makes almost all theories, other than the familiar gauge theories and gravity, inconsistent [74–81].”
Spinning black hole binary dynamics, scattering amplitudes, and effective field theory (2020, background): “Massless and massive helicity methods [46, 47] have proven to be especially effective for calculating four-dimensional amplitudes.”
Scattering of spinning black holes from exponentiated soft factors (2018, methodology): “thors in [24] was simply to show the agreement of the LS method with the previous computations of [21{23]. Moreover, in [24] the new massive spinor-helicity variables of Arkani-Hamed, Huang and Huang [29] were implemented to construct operators carrying spin multipoles. These operators were then mat”
Conformally soft theorem in gauge theory (2019, background): “These greatly constrain, and in some cases completely determine [24,25], all amplitudes.”
The Cosmological Bootstrap: Spinning correlators from symmetries and factorization (2020, background): “In fact, demanding consistency of the four-particle S-matrix leads to powerful constraints on the space of viable quantum field theories [2–4, 87].”
Kerr black holes as elementary particles (2019, neutral): “A convenient on-shell formalism for describing scattering amplitudes for general mass and spin in four dimensions has recently been given in [13].”
Double copy for massive quantum particles with spin (2019, methodology): “up. In that sense, the latter indices can be thought of as o-shell, whereas the little-group indices encode the on-shell spin degrees of freedom. In fact, any scattering amplitude can be represented [78] as having 2ssymmetric indices for each s-spin massive state with momentum p, as carried by the h”
The EFT-hedron (2020, background): “This is the case in four-dimensions with external helicity states [16], where the corresponding orthogonal polynomials are Jacobi polynomials.”