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Hidden Zeros in Exceptional Field Theories from Double Copy

Yang Li, Diederik Roest, Tonnis ter Veldhuis

TL;DR

The paper shows that hidden zeros observed in colour-ordered Tr(Φ^3), the NLSM, and YMS extend to a broader class of theories connected by the double copy. Using KLT, the authors prove that zeros in the single-copy sectors propagate to the double-copy theories GCS, DBI, and the SG subsector, with explicit near-zero factorization into lower-point amplitudes and mixed ext Φ^3 amplitudes. They demonstrate that the zeros are organized by causal diamonds in the kinematic space and persist under various flavour structures, supported by checks up to eight points for YMS. The results unify a family of exceptional scalar EFTs under the double-copy framework and point to new directions, including stringy generalizations and covariant zero loci.

Abstract

It was recently discovered by Arkani-Hamed et al and Cao et al that the colour-ordered scattering amplitudes of Tr$(Φ^3)$, the non-linear sigma model and Yang-Mills-scalar vanish at specific loci. We build on this observation and demonstrate that, beyond colour ordering, scattering amplitudes can display higher-order hidden zeros. A first example are the flavour-paired amplitudes of gravity-coupled scalars, as a double copy of Yang-Mills-scalar. The other two cases are Dirac-Born-Infeld and the special Galileon, which are the natural generalisations of the non-linear sigma model with higher orders of the Adler zero. We demonstrate that the amplitudes of these theories all factorize into lower-point objects in the near-zero limit, and discuss their interpretation. Finally, we comment on the general picture of hidden zeros and prove their relation under the double copy.

Hidden Zeros in Exceptional Field Theories from Double Copy

TL;DR

The paper shows that hidden zeros observed in colour-ordered Tr(Φ^3), the NLSM, and YMS extend to a broader class of theories connected by the double copy. Using KLT, the authors prove that zeros in the single-copy sectors propagate to the double-copy theories GCS, DBI, and the SG subsector, with explicit near-zero factorization into lower-point amplitudes and mixed ext Φ^3 amplitudes. They demonstrate that the zeros are organized by causal diamonds in the kinematic space and persist under various flavour structures, supported by checks up to eight points for YMS. The results unify a family of exceptional scalar EFTs under the double-copy framework and point to new directions, including stringy generalizations and covariant zero loci.

Abstract

It was recently discovered by Arkani-Hamed et al and Cao et al that the colour-ordered scattering amplitudes of Tr, the non-linear sigma model and Yang-Mills-scalar vanish at specific loci. We build on this observation and demonstrate that, beyond colour ordering, scattering amplitudes can display higher-order hidden zeros. A first example are the flavour-paired amplitudes of gravity-coupled scalars, as a double copy of Yang-Mills-scalar. The other two cases are Dirac-Born-Infeld and the special Galileon, which are the natural generalisations of the non-linear sigma model with higher orders of the Adler zero. We demonstrate that the amplitudes of these theories all factorize into lower-point objects in the near-zero limit, and discuss their interpretation. Finally, we comment on the general picture of hidden zeros and prove their relation under the double copy.
Paper Structure (7 sections, 40 equations, 2 figures)

This paper contains 7 sections, 40 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Colour ordering & single zeros
  3. Flavour pairing & double zeros
  4. Single scalar & triple zeros
  5. Hidden zeros and the double copy
  6. Conclusions
  7. Factorization for all choices of the non-zero locus variable

Figures (2)

  • Figure 1: The skinny (red) and square (blue) causal diamonds illustrated in the 6-point kinematic mesh from Arkani-Hamed:2023swr. The colored variables at the bottom and top of the causal diamonds are $X_B$ and $X_T$ mentioned later on in the text.
  • Figure 2: The different theories with zeros, arranged in terms of their soft degree $\sigma$. The underlined theories have no odd vertices and hence the zeros imply their soft behaviours. The vertical dotted lines indicate the increase in zeros for the DC-related theories.