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

TL;DR

HUFT provides a UV‑complete geometric framework that unifies gravity, gauge interactions, and chiral matter on a complexified spacetime, achieved by embedding nonlocal, entire‑function regulators that preserve gauge and diffeomorphism invariance. Through spontaneous breaking, regulator‑modified RG flow, and holomorphic flavon textures controlled by two continuous inputs, the framework predicts the full Standard Model fermion spectrum, CKM and PMNS matrices, and electroweak observables, including a SM‑like Higgs with $m_H\, o125$ GeV and a stable potential up to the nonlocal scale $M_*$. Gauge coupling unification arises as a genuine prediction, with three SM couplings freezing and unifying at $M_{ m GUT} oughly 2.3 imes 10^{16}$ GeV, while hypercharge quantization and anomaly cancellation follow from the holomorphic action. The results agree with PDG2024 within uncertainties using only two inputs, offering a parameter‑economical, predictive path toward a unified description of flavor and fundamental interactions.

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, 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.

Figures (6)

• Figure 1: One‐loop RG evolution of the gauge couplings in HUFT versus the MSSM with $M_{\rm SUSY}=1\,$TeV. Below $M_{\rm GUT}\simeq2.3\times10^{16}$ GeV each coupling runs with its Standard Model $\beta$–function plus smooth decoupling from the $X,Y$ gauge bosons; around $M_{\rm GUT}$ they bend into a narrow unification band and meet, above $M_{\rm GUT}$ the nonlocal form factor $\exp(-\mu^2/M_*^2)$ freezes all $\beta_i$ in the UV. The MSSM curves follow the usual piecewise Standard Model→MSSM running, crossing only by invoking TeV‑scale superpartners and then continuing up to the Planck scale.
• Figure 2: Three‑dimensional surface of the Higgs potential before spontaneous symmetry breaking $V(\phi)$ in the complex $\phi$-plane. The central bulge at $\phi =0$ the local maximum, and the ring of minima at $|\phi|=v$ is the physical vacuum manifold.
• Figure 3: Full Higgs potential after spontaneous symmetry breaking $V(h) \;=\; -\frac{1}{2}\,\mu^2\,(v+h)^2 \;+\;\frac{1}{4}\,\lambda_H\,(v+h)^4$. The solid curve shows the Mexican‑hat shape. The apparent second minimum at $h=−2v$ is the same electroweak vacuum expressed in the opposite gauge orientation $\phi=−v$, there is only one physical vacuum. The maximum at $h=−v$ corresponds to $\phi=0$.
• Figure 4: In the stable scenario our vacuum is in the global minimum of the potential. In the metastable case our vacuum sits in the local minimum while a true, deeper minimum exists. Note: graph not to scale. The local maximum of the classical potential at $H=0$ is too small to be seen here.
• Figure 5: Higgs potential for several temperatures compared with the critical temperature $T_c$. At $T=T_c$ two degenerate minima are separated by a barrier, indicating bubble nucleation and phase coexistence.