Why the Higgs Is Light: The Hierarchy Problem from Threshold Dynamics

The hierarchy problem is one of the most famous puzzles in particle physics. Why is the Higgs boson mass, measured at 125 GeV, so much smaller than the Planck scale at 10¹⁹ GeV? In standard quantum field theory, the Higgs mass receives enormous radiative corrections that naturally drive it to the cutoff scale, requiring extreme fine-tuning or new physics.

This paper presents a resolution from the canvas model, a unified framework in which all physical properties emerge from wave dynamics on a pre-geometric canvas. In this framework, masses are not fundamental parameters. They are determined by coupling eigenvalues under a threshold tensor that arises from the geometric structure of the internal coupling space.

The Higgs is light for a structural reason. It couples to the trace mode of the threshold tensor—the unique eigenvector that is symmetric under all gauge transformations. Fermions align with gauge-modulated subspaces and receive large mass contributions from the strong, weak, and electromagnetic interactions. The Higgs, by contrast, averages over these subspaces and receives only a fraction of the amplification. Its eigenvalue is strictly smaller than all fermion eigenvalues, making it naturally the lightest massive particle in the spectrum.

No new particles are required. No fine-tuning is needed. The hierarchy is protected by the geometry of the internal coupling space, not by a symmetry. The observed Higgs mass corresponds to a threshold proximity parameter consistent with natural expectations.

The paper also predicts percent-level deviations in the Higgs self-coupling, potentially detectable at future colliders such as the High-Luminosity LHC, the Future Circular Collider, or the International Linear Collider.

This result emerges from the canvas model, which also derives the Standard Model gauge group, the three fermion generations, dark matter, and the cosmological constant from first principles.