Upcoming searches for lepton flavour change (LFV) aim to probe New Physics (NP) scales up to ΛNP ∼ 104 TeV, implying that they will be sensitive to NP at lower scales that is suppressed by loops or small couplings. We suppose that the NP responsable for LFV is beyond the reach of the LHC and can be parametrised in Effective Field Theory, introduce a small power-counting parameter λ (à la Cabibbo-Wolfenstein), and assess whether the existing dimension six operator basis and one-loop RGEs provide a good approximation for LFV. We find that μ ↔ e observables can be sensitive to a few dozen dimension eight operators, and to some effects of two-loop anomalous dimensions, for ΛNP ≲ 20 − 100 TeV. We also explore the effect of some simplifying assumptions in the one-loop RGEs, such as neglecting flavour-changing effects.

We propose two models where a U(1) Peccei-Quinn global symmetry arises accidentally and is respected up to high-dimensional operators, so that the axion solution to the strong CP problem is successful even in the presence of Planck-suppressed operators. One model is SU($$ \mathcal{N} $$ N ) gauge interactions with fermions in the fundamental and a scalar in the symmetric. The axion arises from spontaneous symmetry breaking to SO($$ \mathcal{N} $$ N ), that confines at a lower energy scale. Axion quality in the model needs $$ \mathcal{N} $$ N ≳ 10. SO bound states and possibly monopoles provide extra Dark Matter candidates beyond the axion. In the second model the scalar is in the anti-symmetric: SU($$ \mathcal{N} $$ N ) broken to Sp($$ \mathcal{N} $$ N ) needs even $$ \mathcal{N} $$ N ≳ 20. The cosmological DM abundance, consisting of axions and/or super-heavy relics, can be reproduced if the PQ symmetry is broken before inflation (Boltzmann-suppressed production of super-heavy relics) or after (super-heavy relics in thermal equilibrium get partially diluted by dark glue-ball decays).

Neutrino masses are evidence of lepton flavor violation, but no violation in the interactions among the charged leptons has been observed yet. Many models of Physics Beyond the Standard Model (BSM) predict Charged Lepton Flavor Violation (CLFV) in a wide spectrum of processes with rates in reach of upcoming experiments. The experimental searches that provide the current best limits on the CLFV searches are reviewed, with a particular emphasis on the muon-based experiments that give the most stringent constraints on the BSM parameter space. The next generation of muon-based experiments (MEG-II, Mu2e, COMET, Mu3e) aims to reach improvements by many orders of magnitude with respect to the current best limits, thanks to several technological advancements. We review popular heavy BSM theories, and we present the calculations of the predicted CLFV branching ratios, focusing on the more sensitive μ→e sector.

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