Five-point partial waves, splitting constraints and hidden zeros
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| Format: | Preprint |
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2026
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| _version_ | 1866911390187388928 |
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| author | Saha, Arnab Priya Sinha, Aninda |
| author_facet | Saha, Arnab Priya Sinha, Aninda |
| contents | We study the partial-wave expansion of residues of five-point tree-amplitude involving identical scalar particles in the external legs. We check the construction using massive spinor-helicity building blocks and by matching to the tree-level five-point Veneziano amplitude at fixed mass levels. As an application, we express five-point splitting constraints - the reduction of the five-point amplitude to products of four-point amplitudes on special kinematic loci - as linear relations among the five-point partial-wave coefficients. At low mass levels these constraints, together with spin truncation, fix the full five-point partial-wave data in terms of the four-point coefficients and imply simple compatibility conditions; remarkably, imposing two independent splitting loci also forces the residue to vanish on their intersection, making the associated hidden zero manifest in partial-wave space. We also show that once both channels allow spin-2 exchange a genuine kernel can remain, indicating the need for additional higher-point input to achieve complete rigidity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_15088 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Five-point partial waves, splitting constraints and hidden zeros Saha, Arnab Priya Sinha, Aninda High Energy Physics - Theory High Energy Physics - Phenomenology We study the partial-wave expansion of residues of five-point tree-amplitude involving identical scalar particles in the external legs. We check the construction using massive spinor-helicity building blocks and by matching to the tree-level five-point Veneziano amplitude at fixed mass levels. As an application, we express five-point splitting constraints - the reduction of the five-point amplitude to products of four-point amplitudes on special kinematic loci - as linear relations among the five-point partial-wave coefficients. At low mass levels these constraints, together with spin truncation, fix the full five-point partial-wave data in terms of the four-point coefficients and imply simple compatibility conditions; remarkably, imposing two independent splitting loci also forces the residue to vanish on their intersection, making the associated hidden zero manifest in partial-wave space. We also show that once both channels allow spin-2 exchange a genuine kernel can remain, indicating the need for additional higher-point input to achieve complete rigidity. |
| title | Five-point partial waves, splitting constraints and hidden zeros |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2601.15088 |