Structural Origin of Higgs, Electroweak, and Strong-Coupling Scale Relations

This work presents a zero-parameter structural formulation of Higgs, electroweak, Yukawa, and strong-coupling scale relations.Using the fixed ratios\[R=\frac{13}{6}, \qquad S=\frac{31}{24},\]the Higgs-sector base structure is written as\[B_H=12R\alpha^2_{[1\to2]}=12R\alpha^{-2},\qquad\alpha^2_{[i\to j]}\equiv\alpha^{2(i-j)}.\]The Higgs mass and electroweak vacuum expectation value are represented by\[\frac{m_H}{m_e}=\frac{1}{2}B_H+\Psi_H,\qquad\frac{v}{m_e}=B_H-\Psi_v,\]with fixed structural integers \(\Psi_H=712\) and \(\Psi_v=6408\). The resulting structural values are\[m_H\approx125.1116\,\mathrm{GeV},\qquadv\approx246.2210\,\mathrm{GeV},\qquady_e\approx2.935012\times10^{-6}.\]The same sequence gives\[\sin^2\theta_W\approx0.223215,\qquadm_W\approx80.36848\,\mathrm{GeV},\qquadm_Z\approx91.18752\,\mathrm{GeV},\]and the cross-sector boundary relation\[\alpha_s(m_Z)=1-\frac{m_W}{m_Z}\approx0.118646.\] The formulation introduces no observable-specific fitting parameters. The values are compared directly with representative Higgs, electroweak, and strong-coupling reference values, while the QCD running section is treated as an illustrative continuation from the structural boundary value at \(m_Z\). A minimal Python implementation is included in the paper and provided for full reproducibility:https://github.com/yasuotanakaresearch/zero-parameter-structure