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Abstract We study the possibility to generate the quark mass hierarchies as well as the CKM quark mixing and CP violation without fine-tuning in a quark flavour model with modular A 4 symmetry. The quark mass hierarchies are considered in the vicinity of the fixed point τ = i∞, τ being the vacuum expectation value of the modulus. We consider first a model in which the up-type and down-type quark mass matrices M u and M d involve modular forms of level 3 and weights 6, 4 and 2 and each depends on four constant parameters. Two ratios of these parameters, g u and g d , can be sources of the CP violation. If M u and M d depend on the same τ, it is possible to reproduce the up-type and down-type quark mass hierarchies in the considered model for |g u | O 𝓞 (10) with all other constants being in magnitude of the same order. However, reproducing the CP violation in the quark sector is problematic. A correct description of the quark mass hierarchies, the quark mixing and CP violation is possible close to τ = i∞ with all constant being in magnitude of the same order and complex g u and g d , if there are two different moduli τ u and τ d in the up-type and down-type quark sectors. We also consider the case of M u and M d depending on the same τ and involving modular forms of weights 8, 4, 2 and 6, 4, 2, respectively, with M u receiving a tiny SUSY breaking or higher dimensional operator contribution. Both the mass hierarchies of up-type and down-type quarks as well and the CKM mixing angles and CP violating phase are reproduced successfully with one complex parameter and all parameters being in magnitude of the same order. The relatively large value of Im τ, needed for describing the down-type quark mass hierarchies, is crucial for obtaining the correct up-type quark mass hierarchies.

Abstract We analyse the possibility of describing quark masses, mixing and CP violation in S 4 ′ S₄^(′) modular flavour models without flavons. We focus on the case where the closeness of the modulus to the point of residual ℤ 3 ST ℤ₃^(ST) symmetry (the cusp) plays a role in generating quark mass hierarchies and discuss the role modular form normalisations play in such constructions. We find that fitting quark data requires explicit CP breaking, unless a second modulus is introduced.

Soluble sugars, organic acids and volatiles are important components that determine unique fruit flavor and consumer preferences. However, the metabolic dynamics and underlying regulatory networks that modulate overall flavor formation during fruit development and ripening remain largely unknown for most fruit species. In this study, by integrating flavor-associated metabolism and transcriptome data from 12 fruit developmental and ripening stages of Actinidia chinensis cv Hongyang, we generated a global map of changes in the flavor-related metabolites throughout development and ripening of kiwifruit. Using this dataset, we constructed complex regulatory networks allowing to identify key structural genes and transcription factors that regulate the metabolism of soluble sugars, organic acids and important volatiles in kiwifruit. Moreover, our study revealed the regulatory mechanism involving key transcription factors regulating flavor metabolism. The modulation of flavor metabolism by the identified key transcription factors was confirmed in different kiwifruit species providing the proof of concept that our dataset provides a suitable tool for clarification of the regulatory factors controlling flavor biosynthetic pathways that have not been previously illuminated. Overall, in addition to providing new insight into the metabolic regulation of flavor during fruit development and ripening, the outcome of our study establishes a foundation for flavor improvement in kiwifruit.

Abstract Leptoquarks are prime candidates for explaining the intriguing hints for lepton flavour universality violation. In particular, the SU(2) L doublet of scalar leptoquarks S 2 is capable of providing an explanation for the tensions between the measurements and the Standard Model predictions in (g − 2) μ , b → sℓ + ℓ − and b → cτν processes, as well as in non-resonant di-electron production. However, in the minimal setup with a single leptoquark generation, a common explanation for all these issues is not possible as this would lead to unacceptably large charged lepton flavour violation. We therefore propose a model with three generations of S 2, each coupling exclusively to a single lepton flavour, i.e. a model extending the Standard Model particle content by an electroquark, a muoquark and a tauquark. We show that after taking into account other constraints, such as those originating from electroweak precision observables and ∆F = 2 processes, it is possible to provide a combined explanation for all these hints of lepton flavour universality violation. Moreover, we find that the presence of the tauquark can generate a dimension-six O 9 U 𝓞₉ᵁ operator via off-shell photon penguin diagrams, which, together with the muoquark contribution, further improves the global fit to b → sℓ + ℓ − data.

A bstract We study the flavor structure of the lepton and baryon number-conserving dimension-6 operators in the Standard Model effective field theory (SMEFT). Building on the work of [ 1 ], we define several well-motivated flavor symmetries and symmetry-breaking patterns that serve as competing hypotheses about the ultraviolet (UV) dynamics beyond the SM, not far above the TeV scale. In particular, we consider four different structures in the quark sector and seven in the charged lepton sector. The set of flavor-breaking spurions is (almost) always taken to be the minimal one needed to reproduce the observed charged fermion masses and mixings. For each case, we explicitly construct and count the operators to the first few orders in the spurion expansion, providing ready-for-use setups for phenomenological studies and global fits. We provide a Mathematica package SMEFTflavor ( https://github.com/aethomsen/SMEFTflavor ) to facilitate similar analyses for flavor symmetries not covered in this work.

A bstract We build upon a simple U(2) F model of flavor, in which all fermion masses and mixing hierarchies arise from powers of two small parameters controlling U(2) F breaking. In the original formulation, an isomorphism to the discrete D 6 × U(1) F symmetry was invoked to generate a Majorana neutrino mass term. Here, we retain the successful features of that model for the charged leptons and quarks, while exploring alternative neutrino charge assignments within the U(2) F framework. This approach allows us to generate Majorana neutrino masses via the see-saw mechanism without introducing any additional symmetries nor invoking any isomorphism. We further examine the implications of our models for Lepton Flavor Violating (LFV) decays, analyzing the processes μ → eγ , τ → μγ and τ → eγ and their connection with the leptonic anomalous magnetic moments. We show that within the Standard Model Effective Field Theory (SMEFT) approach the current limits on the branching ratios of μ → eγ LFV decays obtained in our U(2) F models are not compatible with the central value of the recent measurement of the ( g − 2) μ , thereby suggesting that either ( g − 2) μ must be very close to the Standard Model predictions, as the latest experimental and theoretical results seem to suggest, or the invoked flavor symmetry is not appropriate to describe an anomalous muon magnetic moment.

A bstract The flavour puzzle is one of the greatest mysteries in particle physics. A ‘flavour deconstruction’ of the electroweak gauge symmetry, by promoting at least part of it to the product of a third family factor (under which the Higgs is charged) times a light family factor, allows one to address the flavour puzzle at a low scale due to accidentally realised U(2) 5 flavour symmetries. The unavoidable consequence is new heavy gauge bosons with direct couplings to the Higgs, threatening the stability of the electroweak scale. In this work, we propose a UV complete model of flavour based on deconstructing only hypercharge. We find that the model satisfies finite naturalness criteria, benefiting from the smallness of the hypercharge gauge coupling in controlling radiative Higgs mass corrections and passing phenomenological bounds. Our setup allows one to begin explaining flavour at the TeV scale, while dynamics solving the large hierarchy problem can lie at a higher scale up to around 10 TeV — without worsening the unavoidable little hierarchy problem. The low-energy phenomenology of the model is dominated by a single Z ′ gauge boson with chiral and flavour non-universal couplings, with mass as light as a few TeV thanks to the U(2) 5 symmetry. The natural parameter space of the model will be probed by the HL-LHC and unavoidably leads to large positive shifts in the W -boson mass, as well as an enhancement in B ( B s,d → μ + μ − ). Finally, we show that a future electroweak precision machine such as FCC-ee easily has the reach to fully exclude the model.

A bstract We study the lepton flavor violation (LFV), the leptonic magnetic moments ( g − 2) μ, e and the electric dipole moment (EDM) of the electron in the Standard-Model Effective Field Theory with the Γ N modular flavor symmetry. We employ the stringy Ansatz on coupling structure that 4-point couplings of matter fields are written by a product of 3-point couplings of matter fields. We take the level 3 finite modular group, Γ 3 for the flavor symmetry, and discuss the dipole operators at nearby fixed point τ = i , where observed lepton masses and mixing angles are well reproduced. Suppose the anomaly of the anomalous magnetic moment of the muon to be evidence of the new physics (NP), we have related it with ( g − 2) e , LFV decays, and the electron EDM. It is found that the NP contribution to ( g − 2) e is proportional to the lepton masses squared likewise the naive scaling. We also discuss the correlations among the LFV processes μ → eγ , τ → μγ and τ → eγ , which are testable in the future. The electron EDM requires the tiny imaginary part of the relevant Wilson coefficient in the basis of real positive charged lepton masses, which is related to the μ → eγ transition in our framework.

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.