What question did this study set out to answer?

This study aims to explore the intrinsic non-locality in glueball decay mechanisms through theoretical predictions and structural analysis.

June 23, 2026Open Access

Intrinsic Non-Locality of Glueball Decay: A Structural Prediction from the Discrete TCH Substrat

Key Points

This study aims to explore the intrinsic non-locality in glueball decay mechanisms through theoretical predictions and structural analysis.
Established glueball mass predictions using the TCH gauge web.
Analyzed glueball decay widths via substrate-level Feshbach theory.
Identified unique characteristics of non-local routing in decay processes.
Predicted glueball masses for scalar and tensor states at 1660 MeV and 2324 MeV, respectively.
Demonstrated decay widths arise from non-local spacing; widths are zero in local approximation.
Identified falsifiable signatures of non-local processes and decay correlations.

Abstract

The companion paper on glueball masses established the universal formula mdressed N = (2N−1)ΛQCD for N-body pure-gauge Fock states on the TCH gauge web, with confirmed predictions for the 0++ scalar (1660 MeV) and 2++ tensor (2324 MeV) glueballs. The substrate-level Feshbach decay width, however, exhibits a 1/ϵregulator dependence indicat- ing that the discrete 208-state Q-spectrum is a step-function approximation to a smooth con- tinuum. Direct diagonalisation of the local Q-matrix reveals four exactly-degenerate eigen- states sitting rigidly at 1ΛQCD (corresponding to the four vertices of a single C4 plaquette, each hosting a single-parity-violation transition). Combined with strong-coupling thresh- old pinning of the dressed pole, this yields the Threshold Bound State Theorem: restricted to the local Hilbert space of a single TCH unit cell, the substrate-level glueball tree-level decay width is identically zero. The empirically observed scalar-glueball width∼100–300 MeV must therefore arise entirely from non-local macroscopic spatial routing: virtual q¯ q ¯ pairs propagating across multiple TCH cells before hadronising into asymptotic ππ/ηη/K K continua. The physical decay is intrinsically non-local in spacetime, not merely strongly- mixed in Hilbert space. We formalise the macroscopic routing programme as Brillouin- zone integration of the momentum-dependent walk operator WQQ(k) over the simple-cubic gauge web, derive phenomenological consequences (scalar-tensor width hierarchy via D-wave angular-momentum suppression, structural explanation of f0-manifold mixing), and identify two falsifiable signatures distinguishing the framework from standard local-vertex glueball treatments: anomalous lattice-volume scaling of glueball widths, and production-decay cor- relations in J/ψ→γG→γππ. 2026-06-20 legacy erratum: This version adds a canon erratum note to the legacy paper. Gauge/spectroscopy claim; check against SMG/TCH continuum status 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.

Intrinsic Non-Locality of Glueball Decay: A Structural Prediction from the Discrete TCH Substrat

Key Points

Abstract

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