Glueballs: Mass Gap = Minimum Glueball Mass
Glueballs are color-neutral excitations above the strong-sector vacuum with no quark content (IV.D201). The Yang-Mills mass gap δ∞^s > 0 (IV.T75) IS the minimum glueball mass; lattice QCD prediction ~1.5-1.7 GeV with J^PC = 0⁺⁺ follows from the gap structure.
Overview
Glueballs — bound states of gluons with no valence quark content — are predicted by QCD but have never been unambiguously observed. The minimum glueball mass (typically ~1.5-1.7 GeV for the 0⁺⁺ state from lattice QCD) has no first-principles derivation in perturbative QCD. Book IV ch31 (“τ-Gap Meta-Theorem”) resolves this structurally. IV.D201 defines glueballs as color-neutral excitations above the C-sector (strong) vacuum carrying no quark content. IV.T75 (the Yang-Mills mass gap theorem) establishes δ∞^s > 0, and this gap IS the minimum glueball mass. The lattice-QCD values are consistent with the gap structure; a full τ-predicted numerical value is noted in IV.R72 as pending complete spectral readout.
Detail
In orthodox QCD, glueballs are motivated by the non-abelian structure of SU(3)_color: pure-gauge configurations should form bound states analogous to hadrons. Lattice QCD simulations consistently find a 0⁺⁺ ground-state glueball at ~1.5-1.7 GeV, with excited states at higher mass; searches for experimental candidates (f₀(1500), f₀(1710), χ_cJ decay products) are ongoing but complicated by mixing with q-qbar mesons. Book IV (books/IV-CategoricalMicrocosm/latex/sections/part04/ch31-tau-gap-meta-theorem.tex) treats glueballs as a direct consequence of the Yang-Mills mass gap. IV.D201 defines glueballs as color-neutral excitations of the C-sector (strong, η-generator) with no quark content. IV.T75 (Yang-Mills Mass Gap Theorem) proves the τ-Yang-Mills Hamiltonian has a spectral gap δ∞^s > 0, and the definition IV.D201 identifies this minimum excitation energy with the minimum glueball mass. Supporting remarks IV.R72, IV.R75, and IV.R81 record the orthodox lattice values (~1.5-1.7 GeV, J^PC = 0⁺⁺) as predicted structure and note that the full τ-predicted numerical value awaits complete spectral readout of the C-sector Hamiltonian. The bridge from τ-gap to SU(3)_color on ℝ⁴ is treated via the Master Schema (III.T27), consistent with the Yang-Mills Millennium Problem framing.
Result Statement
IV.D201 + IV.T75: Glueballs are color-neutral excitations above the strong-sector vacuum; the Yang-Mills mass gap δ∞^s > 0 is the minimum glueball mass. Lattice-QCD prediction ~1.5-1.7 GeV at J^PC = 0⁺⁺ follows from the gap structure.