https://doi.org/10.1140/epjc/s10052-022-11014-4
Regular Article - Theoretical Physics
Toy models for hierarchy studies
Departamento de Física Teórica and IPARCOS, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040, Madrid, Spain
Received:
22
September
2022
Accepted:
5
November
2022
Published online:
18
November
2022
We provide a simple computation in order to estimate the probability of a given hierarchy between two scales. In particular, we work in a model provided with a gauge symmetry, with two scalar doublets. We start from a scale-invariant classical Lagrangian, but by taking into account the Coleman–Weinberg mechanism, we obtain masses for the gauge bosons and the scalars. This approach typically provides a light (L) and a heavy (H) sector related to the two different vacuum expectation values of the two scalars. We compute the size of the hypervolume of the parameter space of the model associated with an interval of mass ratios between these two sectors. We define the probability as proportional to this size and conclude that probabilities of very large hierarchies are not negligible in the type of models studied in this work.
© The Author(s) 2022
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