Hidden zeros for particle/string amplitudes and the unity of colored scalars, pions and gluons
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| Format: | Preprint |
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2023
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| _version_ | 1866929650013306880 |
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| author | Arkani-Hamed, Nima Cao, Qu Dong, Jin Figueiredo, Carolina He, Song |
| author_facet | Arkani-Hamed, Nima Cao, Qu Dong, Jin Figueiredo, Carolina He, Song |
| contents | Recent years have seen the emergence of a new understanding of scattering amplitudes in the simplest theory of colored scalar particles - the Tr$(ϕ^3)$ 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$(ϕ^3)$ amplitudes secretly contain 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$(ϕ^3)$ field theory amplitudes have a hidden pattern of zeros when a special set of non-planar Mandelstam invariants is set to zero. 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 further generalize to the ''stringy'' Tr$(ϕ^3)$ amplitudes. There is 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_16282 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hidden zeros for particle/string amplitudes and the unity of colored scalars, pions and gluons Arkani-Hamed, Nima Cao, Qu Dong, Jin Figueiredo, Carolina He, Song High Energy Physics - Theory High Energy Physics - Phenomenology Recent years have seen the emergence of a new understanding of scattering amplitudes in the simplest theory of colored scalar particles - the Tr$(ϕ^3)$ 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$(ϕ^3)$ amplitudes secretly contain 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$(ϕ^3)$ field theory amplitudes have a hidden pattern of zeros when a special set of non-planar Mandelstam invariants is set to zero. 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 further generalize to the ''stringy'' Tr$(ϕ^3)$ amplitudes. There is 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. |
| title | Hidden zeros for particle/string amplitudes and the unity of colored scalars, pions and gluons |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2312.16282 |