Higgs Sector and Flavour Structure in an Algebraic Three-Generation Model with S3 Family Symmetry
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911627710824448 |
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| author | Gresnigt, Niels |
| author_facet | Gresnigt, Niels |
| contents | We extend our previous algebraic construction of three fermion generations in the complex Clifford algebra $\mathbb{C}\ell(10)$ by incorporating the Higgs sector. Using the $S_3$ family symmetry that permutes three algebraically distinguished fermion sectors, we construct Higgs components as right-action operators and extract the corresponding Yukawa coefficients by means of a trace pairing. This yields two first-generation Higgs doublets with the correct electroweak quantum numbers and a natural Type-II-like separation between down-type and up-type Yukawa channels.
The $S_3$ action triplicates this Higgs sector, producing six Higgs doublets organised into $S_3$-orbits. In the exact $S_3$-invariant limit, the Yukawa sector retains its Type-II structure, while the generation-space Yukawa matrices are not diagonal in the algebraic generation basis. If electroweak symmetry breaking is implemented in the usual way, tree-level flavour-changing neutral currents are not expected in this limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24795 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higgs Sector and Flavour Structure in an Algebraic Three-Generation Model with S3 Family Symmetry Gresnigt, Niels General Physics We extend our previous algebraic construction of three fermion generations in the complex Clifford algebra $\mathbb{C}\ell(10)$ by incorporating the Higgs sector. Using the $S_3$ family symmetry that permutes three algebraically distinguished fermion sectors, we construct Higgs components as right-action operators and extract the corresponding Yukawa coefficients by means of a trace pairing. This yields two first-generation Higgs doublets with the correct electroweak quantum numbers and a natural Type-II-like separation between down-type and up-type Yukawa channels. The $S_3$ action triplicates this Higgs sector, producing six Higgs doublets organised into $S_3$-orbits. In the exact $S_3$-invariant limit, the Yukawa sector retains its Type-II structure, while the generation-space Yukawa matrices are not diagonal in the algebraic generation basis. If electroweak symmetry breaking is implemented in the usual way, tree-level flavour-changing neutral currents are not expected in this limit. |
| title | Higgs Sector and Flavour Structure in an Algebraic Three-Generation Model with S3 Family Symmetry |
| topic | General Physics |
| url | https://arxiv.org/abs/2604.24795 |