Fermion mass hierarchies from vector-like families and possible explanations for the electron and muon anomalous magnetic moments

Abstract

Many great efforts to find an answer on what are the most fundamental particles and forces in our nature have shaped the very important and beautiful theory known as the Standard Model (SM). The observables in the SM are consistent with their experimental bounds with high accuracies. However, many particle physicists agree that the SM is not an ultimate answer to our nature, since there are many observables which can not be addressed by the SM such as mass of neutrinos, a few of well-known anomalies in the SM, the puzzle of the CKM and PMNS mixing matrices, the Dark Matter (DM) and the Dark Energy (DE), etc. In order to bring these interesting topics to understanding of the human beings, it assumes that expansion of the SM is not avoidable and we call this expanded theory “Beyond Standard Model (BSM)”. Many possible BSM models have been suggested to connect with al least one of the listed observables and this idea motivates us to search for physics beyond the SM. Recapitulating the whole story, the SM itself is a great success, however it should be expanded by any means to explain the observables whose mechanisms are not confirmed. We start from this consideration: how can we expand the SM without violating the gauge symmetry and the current experimental bounds for the SM observables. It is evident that the SM must be expanded for the observables which can not be addressed by the SM as discussed above. A possible answer to the question is a minimal extension to the SM and then to study the well-known anomalies and studying the anomalies was a main target over my two works [89, 148]. The other way is to study the FCNC observables within a minimally extended SM, as they are very sensitive to new physics and this approach is a main target of my third project. We made use of the model-dependent approach since there are new operators, which can not be fully replaced by the effective operators appearing in the model-independent approach. As we take the model-dependent approach, it is necessary to extend at least one of the following sectors: SM fermion, scalar and gauge symmetry. An important difference between our first and second (as well as third) work is whether we considered the hierarchical structure of the SM, as we regard the strong hierarchical structure of the SM as a very clear hint at new physics at higher energy scales. A main motivation of our first work is to explain the muon and electron anomalous magnetic moment g − 2 simultaneously. In order to achieve this goal, we extend the SM fermion sector by the fourth vector-like family and the scalar sector by a singlet flavon and the SM gauge symmetry by the local U(1)0 symmetry. Under an assumption that our Z 0 neutral gauge boson only couples to the SM charged leptons, we defined the Z 0 coupling constants by using the mixing formalism in the mass basis. In order to make our analysis as simple as possible, we constrained the relevant mixing angles between ith chiral SM family and 4th vector-like family to be θ12,14,24 for the charged leptons. In this analysis, the mixing angles θ12,14,24 are free parameters and v they are constrained by experimental bounds of the anomalies, the branching ratio of µ → eγ, and neutrino trident production. Using the mass insertion approximation, we distinguished two mass sources, one of which is the chirality flip mass MC 4 whereas the other is the vector-like mass ML 4 . What we found there is increasing the mixing angle θ12 slightly gives an unacceptably high prediction for the branching ratio of the charged lepton flavor violation (CLFV) µ → eγ decay, and this becomes a good motivation to vanish the mixing angle through rest of the analysis. The dominant contribution to each anomaly arises from the Z 0 left-right interactions including an enhancement factor MC 4 /mµ, and the chirality flip mass MC 4 can not increase as much as the vector-like mass ML 4 does, as it is governed by the SM Higgs vev. For this reason, we constrained the chirality flip mass to be ranged from 0 to 200 GeV, and then we found no any value between them can satisfy both anomalies, so leading to a conclusion this BSM model can not explain them simultaneously. Our second BSM model in our second work goes one step further from the first BSM model by implementing the hierarchical structure of the SM in a kinematic way. In order to achieve this goal, we need to assume the SM Lagrangian is the effective Yukawa interactions arising as a result of broken U(1)0 symmetry and what this implement is the general Yukawa interactions can not take place due to the U(1)0 charge. Under this consideration, our second model features that the SM fermions are augmented by two vector-like families and the scalar sector are enlarged by one more SM-like Higgs Hd and a singlet flavon φ and lastly the SM gauge symmetry is extended by the global U(1)0 symmetry (Notice that this U(1)0 is global). One vector-like family can provide two effective seesaw operators, so this is why we introduce two vector-like families, and then all SM generations can acquire their masses. A clear difference between our first and second work is whether we built a mass matrix for each sector of the SM and the construction was done in our second work, so the mixing angles appearing in the second work become a ratio between the Yukawa and vector-like masses. We defined all required mixings, while diagonalizing the mass matrix for the charged lepton sector, and then discussed both anomalies mediated by the SM W gauge boson and by the non-SM scalars at one-loop level. First of all, the W contributions to both anomalies turn out to be too small to its experimental bound, so we conclude another approach is required to explain both anomalies simultaneously and come up with the non-SM scalar exchange at one-loop level and then finally confirm both anomalies can be explained by the non-SM scalar exchange simultaneously. A main motivation of our third work arises from studying the flavor changing neutral currents (FCNCs) to constrain masses of the vector-like family, while keeping the hierarchical structure of the SM implemented in the second work. What we considered especially important is to diagonalize a mass matrix for each fermion sector without any assumptions. For the correct diagonalization, we mainly focus on the second and third generation of the SM at cost of having massless particles in the first SM generation with only one vector-like family. In order to study the FCNC observables, vi we consider the SM Z gauge boson, however it is evident that the SM Z gauge boson can not generate the flavor violating interactions. The SM Z gauge boson can cause the renormalizable flavor violating interactions by extending the SM fermions by the vector-like family and by operating SU(2) violating mixings, and then it can have small non-zero off-diagonal Z coupling constants in the mass basis. Using the defined Z coupling constants in the mass basis, we analyze the charged lepton sector first via the CLFV τ → µγ, τ → 3µ and Z → µτ decays, predicting the singlet or doublet vector-like charged lepton masses. Our numerical predictions are not significantly constrained by the experimental bounds for the CLFV decays, however it comes as the CMS experimental bound for the vector-like doublet charged leptons might be able to exclude our predictions to a significant extent. As for the quark sector, we use the rare t → cZ decay and the CKM mixing matrix and the CKM mixing matrix appears as a challenging observable to fit our predictions. After fitting our prediction to the CKM mixing matrix as much as possible, we confirm that no any point of our predictions is excluded by the experimental bound for the rare t → cZ decay, predicting mass range of vector-like quarks as in the charged leptons. Based on the minimal extension of the SM in my three works, it has confirmed that physics beyond the SM can be explored in simple scenarios, leading to interesting scientific predictions related to the hypothetical particles such as vector-like particles, CP-even and -odd scalars, Z 0 , etc. and these findings can be verified or ruled out in close future experiments.

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