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arXiv · 2312.16282

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

Nima Arkani-Hamed·Qu Cao·Jin Dong·Carolina Figueiredo·Song He
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Abstract

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.

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Nima Arkani-Hamed, Qu Cao, Jin Dong, Carolina Figueiredo, Song He. 2024-12-30. Hidden zeros for particle/string amplitudes and the unity of colored scalars, pions and gluons. https://arxiv.org/abs/2312.16282

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