Modeling O(1) couplings as IID random variables yields a spread distribution with fat power-law tails that widen with the number of couplings, including a 0.29 probability of spread exceeding 100 for 20 unit-normal draws.
Natural Fermion Hierarchies from Random Yukawa Couplings
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abstract
The Standard Model of particle physics requires Yukawa matrices with eigenval- ues that differ by orders of magnitude. We propose a novel way to explain this fact without any small or large parameters. The mechanism is based on the observation that products of matrices of random order one-numbers have hierarchical spectra. The same mechanism can easily account for the hierarchical structure of the quark mixing matrix.
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The Fundaments of Unity: ${\mathcal O}(1)$ Couplings in Quantum Field Theories
Modeling O(1) couplings as IID random variables yields a spread distribution with fat power-law tails that widen with the number of couplings, including a 0.29 probability of spread exceeding 100 for 20 unit-normal draws.