What question did this study set out to answer?

This research aims to derive the mass and width of the rho meson using line graph topology on the 4.8.8 lattice.

June 23, 2026Open Access

The Holographic Circlette: Part 21 — Vector Mesons, Line Graph Topology, and Chiral Consistency on the 4.8.8 Lattice

DED. G. EllimanCatholic University of Mozambique

Key Points

This research aims to derive the mass and width of the rho meson using line graph topology on the 4.8.8 lattice.
Utilized line graph adjacency eigenvalue of the octagonal matter plaquette for calculations.
Analyzed tree-level decay width in relation to experimental values.
Examined the topological duality between electroweak symmetry breaking and color confinement.
Rho meson mass and width derived, with the decay width at 137 MeV showing a -7.9% deviation from experimental values.
The findings align with the KSFR low-energy theorem about pion decay and vector meson mass.
Identified mesons as topological scars of strong interactions, revealing new insights into their properties.

Abstract

We derive the rho meson mass and width from the line graph topology of the 4.8.8 Archimedean lattice. The vector meson mass emerges as the line graph adjacency eigenvalue of the octagonal matter plaquette, automatically satisfying the KSFR low-energy theorem relating the pion decay constant and vector meson mass. The tree-level decay width of 137 MeV agrees with experiment to -7.9%, leaving exactly the room expected for NLO vertex corrections. The topological duality between electroweak symmetry breaking (golden to silver ratio) and colour confinement (silver to golden ratio) reveals that mesons are the unhealed topological scars of the strong interaction. 2026-06-20 legacy erratum: This version adds a canon erratum note to the legacy paper. Vector-meson spectroscopy needs current audit The body is preserved as a historical derivation trail; the erratum note identifies the current ANCHOR/DRIFT status and superseded claims. 2026-06-21 canon refresh: This version incorporates the 2026-06-21 ANCHOR/DRIFT/PTMS canon refresh and rebuilt local PDF.

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