Hidden zeros are equivalent to enhanced ultraviolet scaling and lead to unique amplitudes in Tr(${\varphi }^3$) theory

Abstract

We investigate the hidden amplitude zeros discovered by Arkani-Hamed et al., which describe a non-trivial vanishing of scattering amplitudes on special external kinematics. We first prove that every type of hidden zero is equivalent to what we call a "subset" enhanced scaling under Britto-Cachazo-Feng-Witten shifts, for any rational function built from planar Lorentz invariants $X_{ij}=(p_i+p_{i+1}+\dots +p_{j-1}{)}^2$. This directly applies to Tr(${\varphi }^3$), non-linear sigma model, or Yang-Mills-scalar amplitudes, revealing a novel type of enhanced UV scaling in these theories. We also use this observation to prove the conjecture that Tr(${\varphi }^3$) amplitudes are uniquely fixed by the zeros, up to an overall normalization, when assuming an ordered and local propagator structure and trivial numerators. In the case of Yang-Mills theory, we conjecture the zeros, combined with the Bern-Carrasco-Johansson color-kinematic duality in the form of amplitude relations, uniquely fix the $\lfloor n/2\rfloor$ distinct polarization structures of $n$-point gluon amplitudes. Our approach opens a new avenue for understanding previous similar uniqueness results, and also extending them beyond tree level for the first time.

v3. New stronger result added: proof that all zeros are equivalent to some (non-adjacent) BCFW shift. Added review section. v4. Journal version

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Cited by in corpus (7)

• Surface Kinematics and "The" Yang-Mills Integrand
• On the New Factorizations of Yang-Mills Amplitudes
• Emergence of Unitarity and Locality from Hidden Zeros at One-Loop Order
• Form factors from string amplitudes
• Surface Gauge Invariance, Soft Limits and the Transmutation of Gluons into Scalars
• Positive Geometry for Stringy Scalar Amplitudes
• Smooth Splitting and Zeros from On-Shell Recursion