PreprintCC BY 4.0arXiv
Millicharged particles and the degree-3 Prouhet-Tarry-Escott problem
Abstract
We use geometry to solve a problem in arithmetic relevant for physics. Namely, for any m we find all integer solutions to the equations ∑i=1m xik = ∑i=1m yik, where k ∈ {1,2,3}; this seems to be new for m ≥ 5. In physics, these are the anomaly cancellation conditions for models with m fermions which can be naturally light and carry small electric charges (a.k.a. millicharged or minicharged particles). The small charges arise by kinetic mixing of the Standard Model U(1) gauge symmetry with an unbroken non-chiral (a.k.a. vector-like) U(1) and the masses are suppressed by a spontaneously-broken chiral U(1).
Related
- The Prouhet--Tarry--Escott problem for subsets with small doubling in integral domains
- The rationality problem for hypersurfaces of degree at least five
- The CR Nirenberg Problem, Part II: Existence and Topological Degree
- The Unfair 0-1 Polynomial Problem and High-Degree Trinomials
- Topological transcendence degree and the dimension problem for perfectoid spaces
BibTeX
@misc{gripaios2026millicharged,
title = {{Millicharged particles and the degree-3 Prouhet-Tarry-Escott problem}},
author = {Ben Gripaios},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26092},
eprint = {2610.26092},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26092},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Millicharged particles and the degree-3 Prouhet-Tarry-Escott problem
AU - Ben Gripaios
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26092
UR - https://arxiv.org/abs/2610.26092
AB - We use geometry to solve a problem in arithmetic relevant for physics. Namely, for any m we find all integer solutions to the equations ∑_i=1^m x_i^k = ∑_i=1^m y_i^k, where k ∈ {1,2,3}; this seems to be new for m ≥ 5. In physics, these are the anomaly cancellation conditions for models with m fermions which can be naturally light and carry small electric charges (a.k.a. millicharged or minicharged particles). The small charges arise by kinetic mixing of the Standard Model U(1) gauge symmetry with an unbroken non-chiral (a.k.a. vector-like) U(1) and the masses are suppressed by a spontaneously-broken chiral U(1).
ER -