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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.28608 |
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| _version_ | 1866914608612114432 |
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| author | Barger, Vernon |
| author_facet | Barger, Vernon |
| contents | We interpret the $B$-lattice flavor framework as a compositeness hierarchy: all three fermion generations are elementary chiral fields, but third-generation Yukawa couplings are undressed ($Q=0$), while lighter generations acquire their Yukawa couplings through chains of spin-$0$ subconstituents (``hops'') whose depth is counted by the $\mathbb{Z}_9$ discrete gauge symmetry. The $\mathbb{Z}_9$ charge admits a two-index decomposition $q_9\mapsto(a,b)$ that identifies two hop species ($α$, $β$) and organizes all fundamental scales from $v_{\rm EW}$ to $M_{\rm Pl}$ on a ``ninths ladder'' $Λ\timesε^{n/9}$. The lattice structure yields the CKM and PMNS mixing parameterizations (with all mixing exponents expressible as charge differences $ΔQ$ dressed by a universal Fritzsch--Xing phase shift of $\pm 1/9$), a seesaw benchmark $m_3\simeq 51$~meV, the axion mass window $m_a\sim 7$--$12\;μ$eV, and the prediction $\tanβ\simeq 10$--$16$ (from the chain internal factor combined with the DFSZ-II two-Higgs-doublet structure), all from two parameters ($Λ$ and $ε= 14/75$). Generation-dependent Peccei--Quinn charges restore the axion--photon coupling ($C_{aγ}\simeq 0.6$--$1.0$) from ``back to invisible'' suppression. An illustrative UV realization in terms of hypercolor-confined scalars communicated to the SM by a gauge-invariant messenger chain is presented as an existence proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28608 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generation as Compositeness: A Subconstituent Interpretation of the $B$-Lattice Flavor Hierarchy Barger, Vernon High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Theory We interpret the $B$-lattice flavor framework as a compositeness hierarchy: all three fermion generations are elementary chiral fields, but third-generation Yukawa couplings are undressed ($Q=0$), while lighter generations acquire their Yukawa couplings through chains of spin-$0$ subconstituents (``hops'') whose depth is counted by the $\mathbb{Z}_9$ discrete gauge symmetry. The $\mathbb{Z}_9$ charge admits a two-index decomposition $q_9\mapsto(a,b)$ that identifies two hop species ($α$, $β$) and organizes all fundamental scales from $v_{\rm EW}$ to $M_{\rm Pl}$ on a ``ninths ladder'' $Λ\timesε^{n/9}$. The lattice structure yields the CKM and PMNS mixing parameterizations (with all mixing exponents expressible as charge differences $ΔQ$ dressed by a universal Fritzsch--Xing phase shift of $\pm 1/9$), a seesaw benchmark $m_3\simeq 51$~meV, the axion mass window $m_a\sim 7$--$12\;μ$eV, and the prediction $\tanβ\simeq 10$--$16$ (from the chain internal factor combined with the DFSZ-II two-Higgs-doublet structure), all from two parameters ($Λ$ and $ε= 14/75$). Generation-dependent Peccei--Quinn charges restore the axion--photon coupling ($C_{aγ}\simeq 0.6$--$1.0$) from ``back to invisible'' suppression. An illustrative UV realization in terms of hypercolor-confined scalars communicated to the SM by a gauge-invariant messenger chain is presented as an existence proof. |
| title | Generation as Compositeness: A Subconstituent Interpretation of the $B$-Lattice Flavor Hierarchy |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.28608 |