胶球解释Partial-Width Joint Inversion of X(2370) and the Barrier-Profile Falsification Criterion: A Complementary Analysis to the BESIII Glueball Claim Communication Segment — Complementary Analysis of the X(2370) Partial-Width Spectrum

On 6 August 2026, the BESIII Collaboration announced at ICHEP 2026, in a special plenary report, that the dominant constituent of X(2370) is the pseudoscalar glueball with spin-parity 0⁻⁺. This archive presents a complementary partial-width joint inversion based entirely on published data. Inverse-variance weighting over five independent width measurements yields Γ̄ = 129.6 ± 6.7 MeV (χ² = 2.41/4 dof, p = 0.66). Partial-width budgeting shows that the five observed three-pseudoscalar channels each carry only 5-10% branching fraction, leaving 50-75% of the total width to be carried by unobserved channels — a "broad and flat" spectrum that is the direct mathematical signature of a bare gauge eigenstate without quark skeleton structure. We propose a falsifiable adjudication criterion: any single partial width exceeding 26 MeV (branching fraction above 20%) constitutes evidence for a hybrid-state wrapping layer; all partial widths remaining below 13 MeV supports the bare-mode (pure glueball) interpretation. The deep reading of this criterion is a measurement of the strong-layer barrier profile of the quark skeleton: a hybrid state corresponds to a local barrier thinning created by the quark core (a tunneling shortcut matched to specific decay channels), whereas the bare glueball corresponds to a complete and uniform barrier stack in which each channel's cascade bottleneck differs, naturally flattening the partial-width spectrum. Decay is a cascade tunneling process traversing the hadronic layer (~200 MeV, ~1 fm), the nuclear layer (~8.8 MeV, ~22 fm), and terminating at the atomic layer (13.6 eV, ~28 nm) — the flat partial-width spectrum of X(2370) and the 13.6 eV ionization threshold of hydrogen are the inner and outer readings of one and the same four-layer confinement barrier stack We present a partial-width joint inversion of published X(2370) measurements and a falsifiable decision criterion designed to be independent of the production-rate tension that currently affects absolute branching-fraction comparisons. Inverse-variance weighting of five independent width measurements gives Γ̄ = 129.6 ± 6.7 MeV (χ² = 2.41/4 dof). Partial-width budgeting shows the five observed three-pseudoscalar channels carry only 25-50% of the total width, the remainder requiring unobserved channels — a broad, flat spectrum. We propose the following pre-registered adjudication criterion: any single partial width exceeding 26 MeV (branching fraction above 20%) supports a hybrid-state interpretation; all partial widths below 13 MeV supports the pure glueball interpretation. The criterion operates on partial-width ratios, in which the J/ψ production branching fraction cancels, and is therefore immune to the 12-17-fold tension between measured production rates and lattice QCD predictions. The criterion also has a direct mechanical reading: it probes whether the strong-interaction barrier profile seen by decay products contains a local thinning, which a quark core would produce, or is uniform, as expected for a bare gluonic configuration.KeywordsX(2370); glueball; partial-width ratios; hybrid state discrimination; production-rate tension; cascade tunneling