Hidden zeros for particle/string amplitudes and the unity of colored scalars, pions and gluons

Journal Article · 29 October 2024 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep10(2024)231 · OSTI ID:2479319

Arkani-Hamed, Nima ^[1]; Cao, Qu  ^[2]; Dong, Jin  ^[3]; Figueiredo, Carolina  ^[4]; He, Song  ^[5]

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1. Institute for Advanced Study, Princeton, NJ (United States)
2. Chinese Academy of Sciences (CAS), Beijing (China); Zhejiang University, Hangzhou (China)
3. Chinese Academy of Sciences (CAS), Beijing (China); University of Chinese Academy of Sciences, Beijing (China)
4. Princeton University, NJ (United States)
5. Chinese Academy of Sciences (CAS), Beijing (China); Hangzhou Institute for Advanced Study, UCAS (China); International Centre for Theoretical Physics Asia-Pacific, Beijing (China); Peng Huanwu Center for Fundamental Theory, Anhui (China)

Recent years have seen the emergence of a new understanding of scattering amplitudes in the simplest theory of colored scalar particles — the Tr(Φ³) theory — based on combinatorial and geometric ideas in the kinematic space of scattering data. In this paper we report a surprise: far from the toy model it appears to be, the “stringy” Tr(Φ³) amplitudes secretly contains the scattering amplitudes for pions, as well as non-supersymmetric gluons, in any number of dimensions. The amplitudes for the different theories are given by one and the same function, related by a simple shift of the kinematics. This discovery was spurred by another fundamental observation: the tree-level Tr(Φ³) field theory amplitudes have a hidden pattern of zeros when a special set of non-planar Mandelstam invariants is set to zero. These zeros are not manifest in Feynman diagrams but are made obvious by the connection of these amplitudes to the new understanding of associahedra arising from “causal diamonds” in kinematic space. Furthermore, near these zeros, the amplitudes simplify, by factoring into a non-trivial product of smaller amplitudes. Remarkably the amplitudes for pions and gluons are observed to also vanish in the same kinematical locus. These properties for Tr(Φ³) amplitudes hold and further generalize to the “stringy” Tr(Φ³) amplitudes. The “kinematic causal diamond” picture suggests a unique shift of the kinematic data that preserves the zeros, and this shift is precisely the one that unifies colored scalars, pions, and gluons into a single object. We will focus in this paper on explaining the hidden zeros and factorization properties and the connection between all the colored theories, working for simplicity at tree level. Subsequent works will describe this new formulation for the Non-linear Sigma Model and non-supersymmetric Yang-Mills theory, at all loop orders.

• Research Organization: Institute for Advanced Study, Princeton, NJ (United States)
• Sponsoring Organization: FCT/Portugal; National Natural Science Foundation of China; USDOE Office of Science (SC)
• Grant/Contract Number: SC0009988
• OSTI ID: 2479319
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 10 Vol. 2024; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English