Structural Origin of Neutrino Mass Relations

This work presents a zero-parameter structural formulation of neutrino mass relations.Using the fixed constants\[R = \frac{13}{6}, \qquad S = \frac{31}{24},\]together with the inherited electron-sector quantities\(\alpha\) and \(m_e\), the neutrino masses are expressed as\[\frac{m_{\nu 1}}{m_e}=12S\alpha^4,\qquad\frac{m_{\nu 2}}{m_e}=\left(1+\frac{1}{3R^2}\right)\frac{m_{\nu 1}}{m_e},\qquad\frac{m_{\nu 3}}{m_e}=\left(2+\frac{1}{R}\right)\frac{m_{\nu 1}}{m_e}.\]The resulting mass spectrum is\[m_{\nu 1}c^2 \approx 0.02246\,\mathrm{eV},\quadm_{\nu 2}c^2 \approx 0.02405\,\mathrm{eV},\quadm_{\nu 3}c^2 \approx 0.05529\,\mathrm{eV}.\]with\[\sum m_\nu=0.10180~\mathrm{eV}.\]The corresponding mass-squared differences are\[\Delta m_{21}^2 \approx 7.418\times10^{-5}\,\mathrm{eV}^2,\quad\Delta m_{32}^2 \approx 2.478\times10^{-3}\,\mathrm{eV}^2.\]which are consistent with current oscillation measurements.The formulation introduces no neutrino-sector fitting parameters.The inputs \(\alpha\) and \(m_e\) are inherited from the electron-sector structure, while the neutrino mass hierarchy is determined entirely by the fixed ratios \(R\) and \(S\).The predicted absolute neutrino masses and total neutrino mass provide a direct opportunity for future experimental and cosmological tests. A minimal Python implementation is provided for full reproducibility:https://github.com/yasuotanakaresearch/zero-parameter-structure