Abstract
The emergence of a hierarchy of scales in the case of spontaneous radiative breaking of conformal symmetry is discussed using the example of a simple quantum-field-theory model. The Coleman–Weinberg (C–W) mechanism is implemented in the one-loop approximation of the effective potential of a scalar field interacting with a fermion field. The emergence of a hierarchy between the renormalization scale and the magnitude of the scalar-field vacuum expectation value is shown. An effective model in the vicinity of the effective potential minimum is constructed and the absence of a direct renormalization group transition to the original theory is established. It is shown that measuring the effective model parameters in the infrared region allows us to determine the scale that limits the applicability region of the model.
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Notes
When defining the concept effective theory, we follow the work [3].
Strictly speaking, we will consider the violation of scale invariance, but in this case, the violation of conformal invariance also occurs [8].
The gauge interactions available in the SM are easy to include in the consideration, but this will not affect the main fundamental points discussed below.
A study is being prepared with appropriate analysis.
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ACKNOWLEDGMENTS
We are grateful for fruitful discussions and critical comments of I.V. Anikin and B.N. Latosh.
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Arbuzov, A.B., Voznaya, U.E. & Kopylova, T.V. On the Hierarchy of Scales in Radiative Symmetry Breaking. Phys. Part. Nuclei Lett. 18, 123–127 (2021). https://doi.org/10.1134/S1547477121020047
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DOI: https://doi.org/10.1134/S1547477121020047