Mass-Dependent Spectral Filtering: Empirical Power-Law Scaling in Vector Meson Decay Widths

The suppression of hadronic decay widths in heavy vector mesons is conventionally attributed to the Okubo-Zweig-Iizuka (OZI) rule and asymptotic freedom. While these mechanisms successfully describe individual systems, no unified scaling law has connected light and heavy sectors. We report an empirical power-law relationship for the dimensionless ratio $\eta=\Gamma/m$ across ground-state vector mesons including $\rho(770)$, $\omega(782)$, $K^{*}(892)$, $\phi(1020)$, $J/\Psi$, and $\Upsilon(1s)$, finding $\eta\propto m^{-\beta}$ with $\beta=3.65\pm0.12$ and $R^{2}=0.991$.

Crucially, we derive this exponent from first principles using Compton wavelength scaling in the five-dimensional kernel space of $E8 \to 3D$ icosahedral projections. The constituent quark Compton wavelength $\lambda_C \propto 1/m_q$ determines the spatial extent over which the quark couples to the kernel structure, governing which projection axes are accessible.

The derived geometric dimension $D_{geo}=1+\phi^{2}\approx3.618$ agrees with the empirical $\beta$ within 1%. This framework treats the OZI rule as a geometric consequence rather than a fundamental principle, and makes specific falsifiable predictions for charm and bottom meson branching ratios.

Correspondence: niedzkatie@gmail.com