We have revisited the computations of the flavor violating leptonic decays of the τ and µ leptons into three lighter charged leptons in the Standard Model with non-vanishing neutrino masses. We were driven by a claimed unnaturally large branching ratio predicted for the τ − → µ − + − ( = µ, e) decays [10], which was at odds with the corresponding predictions for the µ − → e − e − e + processes [8]. In contrast with the prediction in [10], our results are strongly suppressed and in good agreement with the approximation done in ref. [8], where masses and momenta of the external particles were neglected in order to deal with the loop integrals. However, as a result of keeping external momenta and masses in the computation of the dominant penguin and box diagrams-we even find slightly smaller branching fractions. Therefore, we confirm that any future observation of such processes would be an unambiguous manifestation of new physics beyond the Standard Model.

The observation of lepton flavor violating processes at colliders could be a clear signal of a nonminimal neutrino sector. We define a 5-parameter model with a pair of TeV fermion singlets and arbitrary mixings with the three active neutrino flavors. Then we analyze several flavor violating transitions ( → γ, ¯ or µ − e conversions in nuclei) and Z →¯ decays induced by the presence of heavy neutrinos. In particular, we calculate all the one-loop contributions to these processes and present their analytic expressions. We focus on the genuine effects of the heavy Majorana masses, comparing the results in that case with the ones obtained when the two heavy neutrinos define a Dirac field. Finally, we use our results to update the bounds on the heavy-light mixings in the neutrino sector.

The search for flavons with a mass of Oð1Þ TeV at current and future colliders might probe low-scale flavor models. We are interested in the simplest model that invokes the Froggatt-Nielsen mechanism with an Abelian flavor symmetry, which includes a Higgs doublet and a Froggatt-Nielsen complex singlet. Assuming a CP conserving scalar potential, there are a CP-even H F and a CP-odd A F flavons with lepton flavor violating (LFV) couplings. The former can mix with the standard-model-like Higgs boson, thereby inducing tree-level LFV Higgs interactions that may be at the reach of the LHC. We study the constraints on the parameter space of the model from low-energy LFV processes, which are then used to evaluate the flavon decay widths and the gg → ϕ → τμ (ϕ ¼ H F ; A F ) production cross section at hadron colliders. After imposing several kinematic cuts to reduce the standard model main background, we find that for m H F about 200-350 GeV, the decay H F → τμ might be at the reach of the LHC for a luminosity in the range 1-3 ab −1 , however, a luminosity of the order of 10 ab −1 would be required to detect the A F → τμ decay. On the other hand, a future 100 TeV pp collider could probe masses as high as Oð10Þ TeV if it reaches an integrated luminosity of at least 20 ab −1 . Therefore, the 100 TeV Collider could work as a flavon factory.

We obtain analytical expressions, both in terms of parametric integrals and Passarino-Veltman scalar functions, for the one-loop contributions to the anomalous weak magnetic dipole moment (AWMDM) of a charged lepton in the framework of the simplest little Higgs model (SLHM). Our results are general and can be useful to compute the weak properties of a charged lepton in other extensions of the standard model (SM). As a by-product we obtain generic contributions to the anomalous magnetic dipole moment (AMDM), which agree with previous results. We then study numerically the potential contributions from this model to the τ lepton AMDM and AWMDM for values of the parameter space consistent with current experimental data. It is found that they depend mainly on the energy scale f at which the global symmetry is broken and the t β parameter, whereas there is little sensitivity to a mild change in the values of other parameters of the model. While the τ AMDM is of the order of 10 −9 , the real (imaginary) part of its AWMDM is of the order of 10 −9 (10 −10 ). These values seem to be out of the reach of the expected experimental sensitivity of future experiments.

We calculate the ratios Rτ/P≡ Γ (τ → Pντ [γ]) /Γ (P → μνμ [γ]) (P = π, K) at one loop following a large-NC expansion where Chiral Perturbation Theory is enlarged by including the lightest resonances and respecting the short-distance behavior dictated by QCD. We find δRτ/π = (0.18 ± 0.57)% and δRτ/K = (0.97 ± 0.58)%, where the uncertainties are induced fundamentally by the counterterms. We test the lepton universality, obtaining |gτ/gμ|π = 0.9964 ± 0.0038 and |gτ/gμ|K = 0.9857 ± 0.0078, and analyze the CKM unitarity, getting results at 2.1σ and 1.5σ from unitarity via |Vus/Vud| and |Vus|, respectively. We also update the search for non-standard interactions in τ decays. As a by-product, we report the theoretical radiative corrections to the τ → Pντ [γ] decay rates: δτπ = −(0.24 ± 0.56)% and δτK = −(0.15 ± 0.57)%.

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Higgs-flavon fields appear as a part of the Froggatt-Nielsen (FN) mechanism, which attempts to explain the hierarchy of Yukawa couplings. We explore the possibility that the 750 GeV diphoton resonance recently reported at the LHC13, could be identified with a low-scale Higgs-flavon field H F and find the region of the parameter space consistent with CMS and ATLAS data. It is found that the extra vector-like fermions of the ultraviolet completion of the FN mechanism are necessary in order to reproduce the observed signal. We consider a standard model (SM) extension that contains two Higgs doublets (a standard one and an inert one) and one complex FN singlet. The inert doublet includes a stable neutral boson, which provides a viable dark matter candidate, while the mixing of the standard doublet and the FN singlet induces flavor violation in the Higgs sector at the tree-level. Constraints on the parameters of the model are derived from the LHC Higgs data, which include the search for the lepton flavor violating decay of the SM Higgs boson h →μτ . It is also found that in some region of the parameter space the model may give rise to a large branching ratio for the H F → hh decay, of the order of 0.1, which could be searched for at the LHC.

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