What question did this study set out to answer?

To determine whether solving the pure Yang-Mills mass gap problem mathematically dictates the physical hadron mass gap in quantum chromodynamics with matter.

August 19, 2026Open Access

The pure Yang-Mills mass gap does not determine the physical hadron mass gap

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Authors

THTan Daniel Fook Hao

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Implication

Theoretical analysis demonstrates that the pure Yang-Mills mass gap cannot determine the full hadron mass gap in quantum field theory, indicating matter data requires independent external input.

Key Points

To determine whether solving the pure Yang-Mills mass gap problem mathematically dictates the physical hadron mass gap in quantum chromodynamics with matter.
Constructed decoupled matter extensions of pure Yang-Mills records using two-level spectator diagonal Hamiltonians with distinct gaps.
Applied spectral calculus for positive commuting self-adjoint operators alongside the triangle inequality to establish a rigorous lower error bound.
Evaluated four standard constructive quantum field theory attached-structure classes and surveyed nine analytic and numerical quantum field theory frameworks.
Proved that any pure-gauge source-only procedure incurs an error of at least (μ₂ - μ₁)/2 on decoupled matter extension gaps μ₁ < μ₂.
Demonstrated that the error bound is sharp and attained by a constant midpoint procedure.
Showed that pure Yang-Mills records alone cannot determine the physical hadron mass gap, explaining why constructive and numerical methods must supply matter data externally.

Cite This Study

Tan Daniel Fook Hao (2026) studied this question.

synapsesocial.com/papers/6a85643903308d306e2d7cbb https://doi.org/10.5281/zenodo.21972331

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Implication

Theoretical analysis demonstrates that the pure Yang-Mills mass gap cannot determine the full hadron mass gap in quantum field theory, indicating matter data requires independent external input.