On the Standard Model Mass Spectrum and Interactions In the Holomorphic Unified Field Theory

Abstract

We present a unified, ultraviolet-finite framework for the full Standard Model particle mass spectrum based on the Holomorphic Unified Field Theory augmented by nonlocal entire-function regulators. Starting from a single holomorphic action on the complexified spacetime manifold \( M^4_{\mathbb{C}} \), with a Hermitian metric unifying gravity, gauge, and matter sectors, we embed exponential regulator insertions to render all loop integrals finite without breaking gauge or diffeomorphism invariance. After spontaneous breaking of the electroweak and grand unified symmetries, analytic expressions for the charged lepton, quark, and neutrino mass matrices are derived in terms of holomorphic Yukawa textures and regulator form factors. A minimal Froggatt-Nielsen flavon sector fixes all \( \mathcal{O}(1) \) coefficients in terms of two continuous inputs. Regulator-suppressed one- and two-loop renormalization group evolution then yields predictions for all fermion masses, CKM and PMNS mixing angles, \( W \) and \( Z \) boson masses, and the Higgs boson mass and self-couplings. Finally, under a mild set of geometric and topological assumptions we show that gauge coupling unification, three chiral families, hypercharge quantization, and the shape of the Higgs potential are genuine predictions of the holomorphic nonlocal framework.