High Energy Particle Physics

    

Shell-Structured Quantized Masses from Soliton Spectrum

Authors: Nigel B. Cook

We present a simple model of two interacting Majorana fermions that, in its bosonizedform, exhibits a soliton spectrum in the strong-coupling regime. When the couplings areappropriately tuned, the masses of the composite bosonic excitations follow a quantizedpattern of the form m_(n,N) ≈ n(N + 1)mZα/(2π), where n is a positive integer (principal quantum number), N is a non-negative integer (shell index), m_Z is the Z-boson mass, and α is the fine-structure constant. This spectrum emerges naturally from the multi-soliton and shell-like excitations in the coupled sine-Gordon model and provides a direct realization of the quantized mass formula proposed in [1] for charged fermions. The result suggests that shell-structured quantization may be a universal feature of strongly coupled fermionic systems with periodic potentials.

Comments: 3 Pages.

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[v1] 2025-12-21 21:14:24

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