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Although the $(g-2)_\mu$ anomaly can be explained by New Physics (NP)involving only muons, a more general flavor structure is usually expected forNP operators in the Standard Model (SM) Effective Field Theory (SMEFT). Inparticular, if one wants to provide a combined explanation of several beyondthe SM effects, like Lepton Flavor Universality (LFU) Violation, as indicatedby the B anomalies, then a strong alignment of the NP operators in flavor spaceis required to satisfy the bounds from observables featuring Lepton FlavorViolation (LFV), like $\mu \to e \gamma$. We derived the tight bound of$10^{-5}$ on the flavor angle in the dipole operator in the charged-lepton massbasis in the SMEFT. We found that misalignment in several operators athigh-scale could spoil the alignment at low-scale, through the RenormalizationGroup Evolution (RGE) of the SMEFT. In particular, it imposes constraints onsome 4-fermions operators. We explored dynamical mechanisms as well as flavorsymmetries to explain this flavor alignment, and illustrated the difficulty toreach it in an explicit NP model. If the $(g-2)_\mu$ anomaly is confirmed, theonly natural explanation seems to lie in the individual lepton numberconservation. If this accidental symmetry of the SM is also present inhigher-order terms in the SMEFT, we are led to conclude that quark and leptonsectors behave quite differently beyond the SM. This proceeding is based onarXiv:2111.13724.

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