Mathematics > Rings and Algebras
arXiv:2409.09033 (math)
[Submitted on 19 Jul 2024 (v1), last revised 16 Jun 2026 (this version, v3)]
Abstract:We develop a general framework of rank-preserving, element-wise matrix transformations for engineering fermion mass hierarchies in theory-space constructions. We prove that preservation of massless modes requires the transformation function to be separable, $g_f(i,j)=g^{(L)}_f(i)g^{(R)}_f(j)$, which in turn enables independent control of left- and right-chiral zero-mode profiles directly at the level of the theory-space mass matrix. This formalism unifies and extends the clockwork mechanism, permits controlled deformation of Kaluza--Klein spectra, and enhances hierarchy generation in GIM-like fine-cancellation scenarios. As a concrete application, we show that in theory-space models for neutrino masses, suitable transformations allow sub-eV light neutrinos to arise from TeV-scale new physics with only $\mathcal{O}(40)$ additional fermionic sites, while remaining consistent with charged-lepton flavor-violation bounds. In contrast, the corresponding untransformed models asymptote at the MeV scale and cannot access the phenomenologically required regime without extreme field multiplicities or hierarchical parameters.
| Comments: | 13 pages, 2 figures, revised version accepted for publication in EPJC |
| Subjects: | Rings and Algebras (math.RA); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph) |
| Cite as: | arXiv:2409.09033 [math.RA] |
| (or arXiv:2409.09033v3 [math.RA] for this version) | |
| https://doi.org/10.48550/arXiv.2409.09033 arXiv-issued DOI via DataCite |
Submission history
From: Aadarsh Singh [view email]
[v1]
Fri, 19 Jul 2024 16:05:35 UTC (9 KB)
[v2]
Tue, 24 Jun 2025 09:37:48 UTC (281 KB)
[v3]
Tue, 16 Jun 2026 05:35:51 UTC (106 KB)
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