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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2406.04234 |
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| _version_ | 1866915118830321664 |
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| author | Rodina, Laurentiu |
| author_facet | Rodina, Laurentiu |
| contents | 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($ϕ^3$), 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($ϕ^3$) 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hidden zeros are equivalent to enhanced ultraviolet scaling and lead to unique amplitudes in Tr($ϕ^3$) theory Rodina, Laurentiu High Energy Physics - Theory 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($ϕ^3$), 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($ϕ^3$) 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. |
| title | Hidden zeros are equivalent to enhanced ultraviolet scaling and lead to unique amplitudes in Tr($ϕ^3$) theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.04234 |