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Theoretical constraints on the couplings of non-exotic minimal \(Z^{\prime}\) bosons. (English) Zbl 1298.81435

Summary: We have combined perturbative unitarity and renormalisation group equation arguments in order to find a dynamical way to constrain the space of the gauge couplings of the so-called “Minimal \(Z^{\prime}\) Models”. We have analysed the role of the gauge couplings evolution in the perturbative stability of the two-to-two body scattering amplitudes of the vector and scalar sectors of these models and we have shown that perturbative unitarity imposes an upper bound that is generally stronger than the triviality constraint. We have also demonstrated how this method quantitatively refines the usual triviality bound in the case of benchmark scenarios such as the U(1)\({}_{\chi}\), the U(1)\({}_{R}\) or the “pure” U(1)\({}_{B-L}\) extension of the Standard Model. Finally, a description of the underlying model structure in Feynman gauge is provided.

MSC:

81V22 Unified quantum theories
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T17 Renormalization group methods applied to problems in quantum field theory

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References:

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