Higgs sector of the Standard model (SM) is replaced by quantum flavor dynamics (QFD), the gauged flavor $SU(3)_f$ symmetry with scale $Λ$. Anomaly freedom requires addition of three $ν_R$. The approximate QFD Schwinger-Dyson equation for the Euclidean infrared fermion self-energies $Σ_f(p^2)$ has the spontaneous-chiral-symmetry-breaking solutions ideal for seesaw: (1) $Σ_f(p^2)=M_{fR}^2/p$ where three Majorana masses $M_{fR}$ of $ν_{fR}$ are of order $Λ$. (2) $Σ_f(p^2)=m_f^2/p$ where three Dirac masses $m_f=m_{(0)}1+m_{(3)}λ_3+m_{(8)}λ_8$ of SM fermions are {\it exponentially suppressed w.r.t. $Λ$}, and {\it degenerate for all SM fermions in $f$}. (1) $M_{fR}$ break $SU(3)_f$ symmetry completely; $m_{(3)},m_{(8)}$ superimpose the tiny breaking to $U(1) \times U(1)$. All flavor gluons thus acquire self-consistently the masses $\sim Λ$. (2) All $m_f$ break the electroweak $SU(2)_L \times U(1)_Y$ to $U(1)_{em}$. Symmetry partners of the composite Nambu-Goldstone bosons are the genuine Higgs particles: (1) Three $ν_{R}$-composed Higgses $χ_i$ with masses $\sim Λ$. (2) Two new SM-fermion-composed Higgses $h_3, h_8$ with masses $\sim m_{(3)}, m_{(8)}$, respectively. (3) The SM-like SM-fermion-composed Higgs $h$ with mass $\sim m_{(0)}$, the effective Fermi scale. $Σ_f(p^2)$-dependent vertices in the electroweak Ward-Takahashi identities imply: The axial-vector ones give rise to the $W$ and $Z$ masses at Fermi scale. The polar-vector ones give rise to the fermion mass splitting in $f$. At the present exploratory stage the splitting comes out unrealistic.
In this proceeding, we highlight the computation of leading fermionic three-loop corrections to electroweak precision observables (EWPOs) accomplished recently. We summarize the numerical analysis and provide an outlook.
We present the analytic calculation of the planar master integrals which contribute to compute the two-loop light-fermion electroweak corrections to the production of a Higgs boson in association with a jet in gluon-gluon fusion. The complete dependence on the electroweak-boson mass is retained. The master integrals are evaluated by means of the differential equations method and the analytic results are expressed in terms of multiple polylogarithms up to weight four.
We study the impact of additional beyond-the-Standard Model (BSM) fermions, charged under the Standard Model (SM) $SU(2)_L \otimes U(1)_Y$ gauge group, on the electroweak phase transition (EWPT) in a 2-Higgs-Doublet-Model (2HDM) of type II. We find that the strength of the EWPT can be enhanced by about 40% compared to the default 2HDM. Therefore, additional light fermions are a useful tool to weaken the tension between increasing mass constraints on BSM scalars and the requirement of additional light scalar degrees of freedom to accommodate a strong first order EWPT. The findings are of partic…
Renormalization and two loop electroweak corrections to lepton anomalous dipole moments in the standard model and beyond (I): heavy fermion contributions
We extend the so-called singlet doublet dark matter model, where the dark matter is an admixture of a Standard Model singlet and a pair of electroweak doublet fermions, by a singlet scalar field. The new portal coupling of it with the dark sector not only contributes to the dark matter phenomenology (involving relic density and direct detection limits), but also becomes important for generation of dark matter mass through its vacuum expectation value. While the presence of dark sector fermions affects the stability of the electroweak vacuum adversely, we find this additional singlet is capable…
We investigate the effect of fermionic electroweak multiplet dark matter models on the stability of the electroweak vacuum using two-loop renormalization group equations (RGEs) and one-loop matching conditions. Such a treatment is crucial to obtain reliable conclusions, compared with one-loop RGEs and tree-level matching conditions. In addition, we find that the requirement of perturbativity up to the Planck scale would give strong and almost mass-independent constraints on the Yukawa couplings in the dark sector. We also evaluate these models via the idea of finite naturalness for the Higgs m…
To realize first-order electroweak phase transition, it is necessary to generate a barrier in the thermal Higgs potential, which is usually triggered by scalar degree of freedom. We instead investigate phase transition patterns in pure fermion extensions of the standard model, and find that additional fermions with mass hierarchy and mixing could develop such barrier and realize strongly first-order phase transition in such models. In the Higgs potential with polynomial parametrization, the barrier can be generated in the following two patterns: (I) positive quadratic term, negative cubic term…
We present a complete calculation of the next-to-next-to-leading (NNLO) electroweak corrections involving closed fermion loops to the $e^+ e^- \to ZH$ process. This has been achieved by using a semi-numerical technique for the two-loop vertex and box diagrams, which is based on Feynman parameters and dispersion relations for one of the two sub-loops. UV divergences are treated with suitable subtraction terms. Numerical results for the unpolarized differential and integrated cross-section at center-of-mass energy $\sqrt{s}=240~\text{GeV}$ are provided. Combining the NNLO contributions with one …
The applicability of the background field method in spontaneously broken gauge theories is examined with new features emphasized. An explicit one loop analysis in the electroweak theory shows that the method can be consistently implemented in the on-shell renormalization scheme, and that the choice of the background gauge cannot be arbitrary and must be fixed in the Landau gauge if one calculates scattering amplitudes involving unphysical Goldstone bosons. Some possible applications are also briefly indicated.
