Abstract
The Minimal Linear sigma Model is a useful theoretical laboratory. One can investigate in a perturbative renormalisable model the properties of the Higgs boson as a pseudo-Goldstone boson, the phenomenological effects of the radial mode of the field texttt {s} which spontaneously breaks the global SO(5) symmetry and the validity of conclusions based on the Effective Field Theory approach with the field texttt {s} in the spectrum, after the decoupling of heavy degrees of freedom. In this paper all those issues are discussed in the framework of the Minimal Linear sigma Model with CP violating phases leading to pseudoscalar components in the effective Standard Model Yukawa couplings. Also the character of the electroweak phase transition in the presence of the field texttt {s} is investigated.
Highlights
After introducing complex Lagrangian parameters, we compare the electron Electric Dipole Moment (EDM) bounds on the imaginary parts of the Wilson coefficients for different dim 5 and dim 6 operators treated as independent with those obtained when they are correlated by the model, pointing out the limitations of the effective description
In section we investigate the following questions, always in the context of the electron EDM bounds on the magnitude of the acceptable CP violation: 1. What are the bounds on the imaginary parts of the different Wilson coefficients, if one assumes that each of them saturates by itself the experimental EDM bound?
We have analysed the electron EDM bounds on the pseudoscalar Yukawa couplings of the top quark in such an EFT
Summary
The global symmetry group of the MLσ M is S O(5)×U (1)X , where the last Abelian factor ensures the correct hypercharge assignment for the SM fields. After introducing our fermion sector, we return to the question of the compatibility of their values with the Coleman-Weinberg calculation Another interesting aspect of the potential in Eq (2.2) is the compatibility of the phenomenologically acceptable range of the parameters with the naturalness and fine-tuning criteria discussed in detail in Ref. In order to derive this bound, it is useful to introduced an effective Higgs-singlet mixing angle sin γeff as the ratio between the cross sections for the gluon fusion production of σ in the MLσ M and for the gluon fusion production of a SM-like scalar hmσ , with mass mσ , sin γeff σ (gg → σ )MLσ M σ (gg → hmσ )SM (2.11) In principle, such a bound should take into account the VLQ loop contributions to gg → σ , whose expressions can be found in Ref. We conclude that the scalar potential parameter range allowed by the phenomenological constraints is in very good agreement with the fine-tuning criteria discussed earlier
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