ℤ3 and S3 gaugings of ℤN×ℤ'N non-invertible symmetries: quark texture zeros and phenomenology
Abstract
We investigate texture zeros in the quark Yukawa matrices arising from the ℤ3 and S3 gauging of ℤN×ℤ'N, associated with the non-invertible Δ(3N2) and Δ(6N2) symmetries, respectively. We construct the equivalence classes and their fusion rules and use them as selection rules for the Yukawa interactions. We systematically classify the full-rank quark Yukawa textures generated by the two gaugings for N=2,3,4, and $5$. The two gaugings yield the same texture spectrum for N=2 and N=4, whereas the S3 gauging produces additional textures for N=3 and N=5. We further analyze the most restrictive texture pairs compatible with quark data and find that there are at most nine zeros in these texture pairs. For up- and down-quark mass matrices with a total of nine texture zeros, one sector is allowed to contain six zeros while the other contains three, or one contains five zeros while the other contains four. The former case has been studied in previous works. We perform numerical fits for the latter and find it consistent with experimental data. Some viable textures also admit real quark-mass determinants while retaining a physical CKM phase, suggesting a possible connection to the strong CP problem.
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BibTeX
@misc{jiang2026ℤ3,
title = {{$\mathbbZ_3$ and $S_3$ gaugings of $\mathbbZ_N\times\mathbbZ'_N$ non-invertible symmetries: quark texture zeros and phenomenology}},
author = {Zheng Jiang and Bu-Yao Qu and Gui-Jun Ding},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28267},
eprint = {2610.28267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28267},
}
RIS
TY - UNPB
TI - ℤ_3 and S_3 gaugings of ℤ_N×ℤ'_N non-invertible symmetries: quark texture zeros and phenomenology
AU - Zheng Jiang
AU - Bu-Yao Qu
AU - Gui-Jun Ding
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28267
UR - https://arxiv.org/abs/2610.28267
AB - We investigate texture zeros in the quark Yukawa matrices arising from the ℤ_3 and S_3 gauging of ℤ_N×ℤ'_N, associated with the non-invertible Δ(3N^2) and Δ(6N^2) symmetries, respectively. We construct the equivalence classes and their fusion rules and use them as selection rules for the Yukawa interactions. We systematically classify the full-rank quark Yukawa textures generated by the two gaugings for N=2,3,4, and $5$. The two gaugings yield the same texture spectrum for N=2 and N=4, whereas the S_3 gauging produces additional textures for N=3 and N=5. We further analyze the most restrictive texture pairs compatible with quark data and find that there are at most nine zeros in these texture pairs. For up- and down-quark mass matrices with a total of nine texture zeros, one sector is allowed to contain six zeros while the other contains three, or one contains five zeros while the other contains four. The former case has been studied in previous works. We perform numerical fits for the latter and find it consistent with experimental data. Some viable textures also admit real quark-mass determinants while retaining a physical CKM phase, suggesting a possible connection to the strong CP problem.
ER -