Independent chiral control in theory-space models: a rank-preserving framework and its application to neutrino mass generation

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, $$g_f(i,j)=g^{(L)}_f(i)g^{(R)}_f(j)$$ g f ( i , j ) = g f ( L ) ( i ) g f ( R ) ( 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 $$\mathcal {O}(40)$$ 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.