Toy models for hierarchy studies

• Published in: The European physical journal. C, Particles and fields Vol. 82; no. 11; pp. 1046 - 9
• Main Authors: Álvarez-Luna, Clara, Cembranos, José A. R., Sanz-Cillero, Juan José
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-11-2022; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Astronomy; Astrophysics and Cosmology; Bosons; Elementary Particles; Hadrons; Heavy Ions; Hierarchies; Mass ratios; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Probability; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Scalars; String Theory; Symmetry; Theoretical physics
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-022-11014-4

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.