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Is the $(g-2)_μ$ anomaly a threat to Lepton Flavor Conservation?

Although the $(g-2)_μ$ anomaly can be explained by New Physics (NP) involving only muons, a more general flavor structure is usually expected for NP operators in the Standard Model (SM) Effective Field Theory (SMEFT). In particular, if one wants to provide a combined explanation of several beyond the SM effects, like Lepton Flavor Universality (LFU) Violation, as indicated by the B anomalies, then a strong alignment of the NP operators in flavor space is required to satisfy the bounds from observables featuring Lepton Flavor Violation (LFV), like $μ\to e γ$. We derived the tight bound of $10^{-5}$ on the flavor angle in the dipole operator in the charged-lepton mass basis in the SMEFT. We found that misalignment in several operators at high-scale could spoil the alignment at low-scale, through the Renormalization Group Evolution (RGE) of the SMEFT. In particular, it imposes constraints on some 4-fermions operators. We explored dynamical mechanisms as well as flavor symmetries to explain this flavor alignment, and illustrated the difficulty to reach it in an explicit NP model. If the $(g-2)_μ$ anomaly is confirmed, the only natural explanation seems to lie in the individual lepton number conservation. If this accidental symmetry of the SM is also present in higher-order terms in the SMEFT, we are led to conclude that quark and lepton sectors behave quite differently beyond the SM. This proceeding is based on arXiv:2111.13724.