Number Theory in Quantum Physics: Minicharged Particles and the Prouhet-Tarry-Escott Problem
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917375726583808 |
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| author | Lee, Junseok Takahashi, Fuminobu Tsai, Yu-Dai |
| author_facet | Lee, Junseok Takahashi, Fuminobu Tsai, Yu-Dai |
| contents | In quantum gauge theories, anomaly cancellation severely restricts the allowed patterns of chiral charges. Here we show that, in a phenomenologically motivated framework for light minicharged particles, the anomaly cancellation conditions are equivalent to the degree $k=3$ Prouhet-Tarry-Escott problem in number theory. This correspondence immediately implies that the hidden sector must contain at least four minicharged states. For constructions based on minimal ideal solutions, the mass spectrum generically exhibits a near-degenerate doublet structure, so that the discovery of one minicharged particle would point to a partner state with the same minicharge and a nearby mass. Our results uncover an unexpected link between quantum consistency and number theory, with direct implications for model building and future searches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12320 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Number Theory in Quantum Physics: Minicharged Particles and the Prouhet-Tarry-Escott Problem Lee, Junseok Takahashi, Fuminobu Tsai, Yu-Dai High Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics High Energy Physics - Experiment High Energy Physics - Theory Mathematical Physics In quantum gauge theories, anomaly cancellation severely restricts the allowed patterns of chiral charges. Here we show that, in a phenomenologically motivated framework for light minicharged particles, the anomaly cancellation conditions are equivalent to the degree $k=3$ Prouhet-Tarry-Escott problem in number theory. This correspondence immediately implies that the hidden sector must contain at least four minicharged states. For constructions based on minimal ideal solutions, the mass spectrum generically exhibits a near-degenerate doublet structure, so that the discovery of one minicharged particle would point to a partner state with the same minicharge and a nearby mass. Our results uncover an unexpected link between quantum consistency and number theory, with direct implications for model building and future searches. |
| title | Number Theory in Quantum Physics: Minicharged Particles and the Prouhet-Tarry-Escott Problem |
| topic | High Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics High Energy Physics - Experiment High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2603.12320 |