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Hidden zeros are equivalent to enhanced ultraviolet scaling and lead to unique amplitudes in Tr($\phi^3$) theory
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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 $X_{ij}{=}(p_i{+}p_{i+1}{+}\ldots{+}p_{j-1})^2$. This directly applies to Tr($\phi^3$), 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($\phi^3$) 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.
Forward citations
Cited by 8 Pith papers
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Hidden zeros and smooth splitting in Tr phi^3, NLSM, YMS, and the special Galileon are shown to follow from on-shell recursion under improved UV falloff, yielding generalized, triple, and 4d helicity zeros.
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Algebraic versus physical uniqueness of MHV gravity numerators
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Differential operators on scalar-scaffolded variables extract individual phi^3 diagrams from gluon amplitudes, and the independent mixed amplitudes are counted by Catalan numbers.
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All zeros of (super)String Theory
Scaffolding from the tachyon to higher-level string states preserves and extends the hidden zeros of string amplitudes, with extra supersymmetric zeros from the superstring.
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Universality of Colored Scalars from the Stringy KLT Kernel
Pion and colored scalar amplitudes are two readings of the same inverse KLT kernel, related by the alpha-prime shift.
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On the New Factorizations of Yang-Mills Amplitudes
Tree-level Yang-Mills amplitudes factorize into gluings of lower-point amplitudes when a rectangular set of Mandelstam variables vanishes, and this paper gives a rigorous CHY-based proof.
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