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This review considers models with extended Higgs sectors in which there are tree-level flavor-changing neutral currents (FCNC) mediated by scalars. After briefly reviewing models without tree-level FCNC, several models with such currents are discussed. A popular mass-matrix ansatz, in which the flavor-changing couplings are the geometric mean of the individual flavor couplings, is presented. While it provided a target for experimentalists for three decades, it is now being severely challenged by experiments. Couplings expected to be of $O(1)$ must be substantially smaller and the ansatz is now not favored. The minimal flavor violation hypothesis is introduced. Then specific models are presented, including the Branco–Grimus–Lavoura models. These models are not yet excluded experimentally, but they are highly predictive and will be tested once heavy Higgs bosons are discovered. We then turn to flavorful models and flavor-changing decays of heavy Higgs bosons, and it is shown that in many of these models, the heavy Higgs could predominantly decay in a flavor-changing manner (such as $ct$ or $\mu \tau$) and experimentalists are encouraged to include these possibilities in their searches.

We discuss aspects of a promising top-down origin of flavor symmetries in particle physics. Modular transformations originating from string theory dualities are shown to play a crucial role. We introduce the notion of an “eclectic” flavor scheme that unifies traditional flavor symmetries, modular symmetries and ${𝒞}{𝒫}$-transformations. It exhibits the phenomenon of “Local Flavor Unification” with enhanced flavor symmetries at fixed points or lines in moduli space. Successful fits of masses and mixing angles of quarks and leptons are found in the vicinity of these points and lines.

In this paper, recent results in the B-physics field achieved using proton–proton collision data at $\sqrt{s}=8$ and $13$ TeV collected by CMS are presented. They include the angular analysis of the decay $B^{+}\to K^{\ast +}{\mu }^{+}{\mu }^{-}$ with Run 1 data, new measurements of D and B meson production cross-sections and CP violation studies using $B_s^0$ decays with Run 2 data. The results are compared with the Standard Model predictions. A measurement of the CP-violating phase ${\varphi }_s$ achieved by combining results from both Run 1 and Run 2 data is also presented.

The Fierz transformations (Ft) for SU(2) and SU(3) operators in eighth-order fermion interactions are derived. These terms appear in expansions in terms of fermion currents of the following form: I₁ I₂ I₃ I₄ and also the composite , where Γ⁽ⁱ⁾ are either the SU(2) Pauli matrices or SU(3) Gell-Mann matrices. The calculation is carried out using the exchange projector operators.

The current status of flavored dark matter (DM) is reviewed. We discuss the main experimental constraints on models of flavored DM and survey some possible considerations which are relevant for the constructions of models. We then review the application of existing flavor principles to DM, with an emphasis on minimal flavor violation, and discuss implications of flavored DM on collider phenomenology.

Gauge-invariant perturbation theory is an extension of ordinary perturbation theory which describes strictly gauge-invariant states in theories with a Brout–Englert–Higgs effect. Such gauge-invariant states are composite operators which have necessarily only global quantum numbers. As a consequence, flavor is exchanged for custodial quantum numbers in the Standard Model, recreating the fermion spectrum in the process. Here, we study the implications of such a description, possibly also for the generation structure of the Standard Model.

In particular, this implies that scattering processes are essentially bound-state–bound-state interactions, and require a suitable description. We analyze the implications for the pair-production process $e^{+}{e}^{-}\to \bar{f}f$ at a linear collider to leading order. We show how ordinary perturbation theory is recovered as the leading contribution. Using a PDF-type language, we also assess the impact of sub-leading contributions. To lowest order, we find that the result is mainly influenced by how large the contribution of the Higgs at large $x$ is. This gives an interesting, possibly experimentally testable, scenario for the formal field theory underlying the electroweak sector of the Standard Model.

Several recent key results from the BABAR experiment are presented, most using 383.6 fb⁻¹ of data. In particular, the search for B⁺ → τ⁺ν, inclusive and exclusive measurements of |V_ub|, measurements of b → dγ decays and new observations of rare charmless hadronic decays. The new results provide important experimental constraints on the Standard Model and new physics models.

The use of the binary tetrahedral group (T′) as flavor symmetry is discussed. I emphasize the CKM quark and PMNS neutrino mixings. I present a novel formula for the Cabibbo angle.

Fermion mass generation in the standard model was invented by Weinberg, while it is an old notion that strong Yukawa coupling could be the agent of electroweak symmetry breaking. Observation of the 126 GeV boson has crashed the prospects for such a heavy chiral quark doublet Q. However, the dilaton possibility can only be ruled out by confirming vector boson fusion with Run 2 data at the LHC, which starts only in 2015. We recast the condensation scenario as Fermi–Yang model v2.0. A Gap Equation has been constructed, with numerical solution demonstrating dynamical m_Q generation; scale invariance of this equation may be consistent with a dilaton. Other consequences to be checked are "annihilation stars," and enhanced B_d →μ⁺μ^-, K_L →π⁰νν, and possibly sin ϕ_s. If verified in Nature, the Agent of BEH mechanism would differ from current perception, the 126 GeV boson would be the first New Physics at the LHC, and we would have enough CP violation for baryogenesis.

We discuss aspects of a promising top-down origin of flavor symmetries in particle physics. Modular transformations originating from string theory dualities are shown to play a crucial role. We introduce the notion of an “eclectic” flavor scheme that unifies traditional flavor symmetries, modular symmetries and 𝒞𝒫-transformations. It exhibits the phenomenon of “Local Flavor Unification” with enhanced flavor symmetries at fixed points or lines in moduli space. Successful fits of masses and mixing angles of quarks and leptons are found in the vicinity of these points and lines.