The origin of fermion generations is one of the great mysteries in particle physics. We consider here a possible solution within the Standard Model framework based on a nonabelian generalization of electric-magnetic duality. First, nonabelian duality says that dual to the colour (electric) symmetry SU(3), there is a ``colour magnetic symmetry'' $\widetilde{SU}(3)$, which by a result of 't~Hooft is spontaneously broken and can thus play the role of the "horizontal symmetry" of generations. Second, nonabelian duality suggests the manner this symmetry is broken with frame vectors in internal symmetry space acting as Higgs fields. As a result, mass matrices factorize leading to fermion mass hierarchy. A calculation to first order gives mixing (CKM and MNS) matrices in general agreement with experiment. In particular, quark mixing is seen naturally to be weak compared with leptons, while within the lepton sector, $\mu-\tau$ mixing turns out near maximal but $e-\tau$ mixing small, just as seen in recent $\nu$ oscillation experiments. In addition, the scheme leads to many testable predictions ranging from rare FCNC meson decays and $\mu-e$ conversion in nuclei to cosmic ray air showers above $10^{20}$ eV.

The Standard Model (SM) of particle physics fails to explain the observed hierarchy in fermion masses or the origin of fermion-flavor structure. We construct a model to explain these observations in the quark sector. We introduce a spectrum of new particles consisting of six of each — massive singlet vector-like quarks (VLQs), singlet scalars, and SU(2)-doublet scalars. SM quark masses are generated when the neutral components of the SU(2)-doublet scalars acquire non-zero vacuum expectation values (VEVs). We impose global symmetries to ensure that Yukawa couplings stay roughly flavor diagonal and democratic (of the same order), as well as to suppress tree-level flavor-changing neutral currents. Quark-mass hierarchy then follows from a hierarchy in scalar VEVs. The singlet scalars also acquire weak-scale VEVs. Together with the VLQs, they act as messengers between different generations of quarks in the SM. These messenger particles are responsible for generating the elements of the Cabibbo-Kobayashi-Masakawa (CKM) matrix which depend on the ratios of the singlet VEVs and VLQ masses. Constructed this way, the CKM matrix is found to be independent of the SM fermion masses. Using the measured values of the CKM matrix elements and assuming order-one couplings, we derive constraints on the masses of the VLQs and discuss prospects for probing our model in the near future.

The neutrino sector offers one of the most sensitive probes of new physics beyond the Standard Model of Particle Physics (SM). The mechanism of neutrino mass generation is still unknown. The observed suppression of neutrino masses hints at a large scale, conceivably of the order of the scale of a rand unified theory (GUT), which is a unique feature of neutrinos that is not shared by the charged fermions. The origin of neutrino masses and mixing is part of the outstanding puzzle of fermion masses and mixings, which is not explained ab initio in the SM. Flavor model building for both quark and lepton sectors is important in order to gain a better understanding of the origin of the structure of mass hierarchy and flavor mixing, which constitute the dominant fraction of the SM parameters. Recent activities in neutrino flavor model building based on non-Abelian discrete flavor symmetries and modular flavor symmetries have been shown to be a promising direction to explore. The emerging models provide a framework that has a significantly reduced number of undetermined parameters in the flavor sector. In addition, such a framework affords a novel origin of C P violation from group theory due to the intimate connection between physical C P transformation and group theoretical properties of non-Abelian discrete groups. Model building based on non-Abelian discrete flavor symmetries and their modular variants enables the particle physics community to interpret the current and anticipated

A Hexad Preon model where leptons, quarks and W Z bosons are composite is proposed. Six Hexad Preons transform under $U(3)\otimes U(3)$ local gauge theory which is identified with $U(1)_Q\otimes SU(3)_C\otimes SU(3)_f\otimes U(1)_w$. All salient features of the standard model can be obtained from the compositeness of leptons and quarks: There are exactly six quarks and six leptons with evident three families (generations); All quantum numbers of leptons and quarks can be given out of that of preons; QED and QCD are given by electro-strong interaction $U(1)_Q\otimes SU(3)_C$ ; The weak interaction is residual "Van der Waals" forces between preons and dipreons. It is shown that all processes in standard model are just reshuffle of preons. In addition, a possible dark matter candidate is presented. Other questions like the electroweak symmetry breaking, the spin of fermions, the origin of quark and lepton mixing, \textit{etc.}, are also addressed.

Active neutrino masses are extremely smaller than those of other quarks and leptons, and there are large flavor mixings in the lepton sector contrary to the quark sector. They are great mysteries in the standard model, which are also excellent hints of new physics beyond the stand model. Thus, questions “What is an origin of tiny neutrino mass?” and “What is an origin of large lepton flavor mixings?” are very important. There have been a lot of theoretical trials to answer the questions. This talk is a brief overview of researches of origins of tiny neutrino mass and large flavor mixings in the lepton sector. I give clear explanations of seesaw mechanism [1], effects of quantum corrections [2,3], neutrinophilic Higgs doublet model [4,5], grand unified model [6,7], and so on.

We rewrite the Yukawa interactions of the Standard Model in terms of flavor-dependent vacuum structure to address the family mass hierarchy and CP violation in both the quark sector and lepton sector. It is realized that Yukawa terms only include the same number of degrees of freedom as phenomenological observables with no requirement of extra particle or any new symmetry. The quark and lepton mass hierarchy arises as a natural result of the close-to-flat vacuum in flavor space. The CP violations in CKM mixing and PMNS mixing are explained as general quantum phases between weak gauge eigenstates and Yukawa interaction states. The mechanism is proven by reproduction of all current quark/lepton mass data and the CKM/PMNS mixing parameters.

We rewrite the Yukawa interactions of the standard model in terms of flavour-dependent vacuum structure to address the family mass hierarchy and CP violation in both the quark sector and lepton sector. It is realized for the first time that the Lagrangian only includes the same number of degrees of freedom as phenomenological observables with no requirement of extra particles or any new symmetry. The quark and lepton mass hierarchy arises as a natural result of the close-to-flat vacuum in flavou

Flavor remains one of the most successful yet least understood structures of the Standard Model. The discovery of the Higgs boson completed the electroweak account of mass generation, but did not explain the origin of fermion families, mass hierarchies, or mixing patterns. In this sense, flavor can be regarded as an empirically successful but conceptually incomplete structure. Neutrinos occupy a particularly sensitive place within this problem: their masses are tiny, their mixing is large, and their mass-generation mechanism may differ from that of charged fermions. In this article, we discuss flavor as an open conceptual problem and argue that DUNE, as a phased program spanning precision oscillation measurements and sensitivity to BSM and dark-sector phenomena, provides a powerful framework for testing the self-consistency and possible limits of the present three-flavor description. In particular, the complementarity between the long-baseline program and the Phase I near-detector complex, together with the DUNE-PRISM strategy for controlling interaction-model systematics and enabling data-driven near-to-far predictions, makes DUNE especially well-suited to search for small, correlated departures from the minimal flavor framework.

Abstract We propose a tri-hypercharge (TH) extension of the Standard Model (SM) in which a separate gauged weak hypercharge is associated with each fermion family. In this way, every quark and lepton multiplet carries unique gauge quantum numbers under the extended gauge group, providing the starting point for a theory of flavour. If the Higgs doublets only carry third family hypercharge, then only third family renormalisable Yukawa couplings are allowed. However, non-renormalisable Yukawa couplings may be induced by the high scale Higgs fields (hyperons) which break the three hypercharges down to the SM hypercharge, providing an explanation for fermion mass hierarchies and the smallness of CKM quark mixing. Following a similar methodology, we study the origin of neutrino masses and mixing in this model. Due to the TH gauge symmetry, the implementation of a seesaw mechanism naturally leads to a low scale seesaw, where the right-handed neutrinos in the model may be as light as the TeV scale. We present simple examples of hyperon fields which can reproduce all quark and lepton (including neutrino) masses and mixing. After a preliminary phenomenological study, we conclude that one of the massive Z′ bosons can be as light as a few TeV, with implications for flavour-violating observables, LHC physics and electroweak precision observables.

The origin of fermion mass hierarchies and mixings is one of the unresolved and most difficult problems in high-energy physics. One possibility to address the flavour problems is by extending the standard model to include a family symmetry. In the recent years it has become very popular to use non-Abelian discrete flavour symmetries because of their power in the prediction of the large leptonic mixing angles relevant for neutrino oscillation experiments. Here we give an introduction to the flavour problem and to discrete groups that have been used to attempt a solution for it. We review the current status of models in light of the recent measurement of the reactor angle, and we consider different model-building directions taken. The use of the flavons or multi-Higgs scalars in model building is discussed as well as the direct versus indirect approaches. We also focus on the possibility of experimentally distinguishing flavour symmetry models by means of mixing sum rules and mass sum rules. In fact, we illustrate in this review the complete path from mathematics, via model building, to experiments, so that any reader interested in starting work in the field could use this text as a starting point in order to obtain a broad overview of the different subject areas.

left-handed and right-handed quarks and leptons of the ith generation, λ u,d,e i j {\displaystyle \lambda _{\text{u,d,e}}^{i\,j}} are matrices of Yukawa couplings The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson that couples to (interacts with) particles whose mass arises from their interactions with the Higgs field, ha In July 2017, CERN confirmed that all measurements still agree with the predictions of the Standard Model, and called the discovered particle simply "the Higgs boson". As of 2019, the Large Hadron Collider has continued to produce findings that confirm the 2013 understanding of the Higgs field and particle. The LHC's experimental work since restarting in 2015 has included probing the Higgs field and boson to a greater level of detail, and confirming whether less common predictions were correct. In particular, exploration since 2015 has provided strong evidence of the predicted direct decay into fermions such as pairs of bottom quarks (3.6 σ) – described as an "important milestone" in understanding its short lifetime and other rare decays – and also to confirm decay into pairs of tau leptons (5.9 σ). This was described by CERN as being "of paramount importance to establishing the coupling of the Higgs boson to leptons and represents an important step towards measuring its couplings to third generation fermions, the very heavy copies of the electrons and quarks, whose role in nature is a profound mystery". Published results as of 19 March 2018 at 13 TeV for ATLAS and CMS had their measurements of the Higgs mass at 124.98±0.28 GeV/c2 and 125.26±0.21 GeV/c2 respectively. In July 2018, the ATLAS and CMS experiments reported observing the Higgs boson decay into a pair of bottom quarks, which makes up approximately 60% of all of its decays. where ( d , u , e , ν ) L,R i {\displaystyle (d,u,e,\nu )_{\text{L,R}}^{i}} are left-handed and right-handed quarks and leptons of the ith generation, λ u,d,e i j {\displaystyle \lambda _{\text{u,d,e}}^{i\,j}} are matrices of Yukawa couplings where h.c. denotes the hermitian conjugate of all the preceding terms. In the symmetry breaking ground state, only the terms containing …

Abstract We explore the possibility that the semi-leptonic B decay ratios RK* $$ {R}_{K^{\left(*\right)}} $$ which violate μ − e universality are related to the origin of the fermion Yukawa couplings in the Standard Model. Some time ago, a vector-like fourth family (without a Z′) was used to generate fermion mass hierarchies and mixing patterns without introducing any family symmetry. Recently the idea of inducing flavourful Z′ couplings via mixing with a vector-like fourth family which carries gauged U(1)′ charges has been proposed as a simple way of producing controlled flavour universality violation while elegantly cancelling anomalies. We show that the fusion of these two ideas provides a nice connection between RK* $$ {R}_{K^{\left(*\right)}} $$ and the origin of Yukawa couplings in the quark sector. However the lepton sector requires some tuning of Yukawa couplings to obtain the desired coupling of Z′ to muons.