The Silence of the Dipoles: Accidental Symmetries in Lepton Flavor

Upcoming experiments are set to dramatically improve the search for charged lepton flavor violation, with the sensitivity to the rates of $\mu \to eee$ decay and $\mu N\to eN$ conversion expected to improve by four orders of magnitude in the near future. We study how these measurements reshape our understanding of fundamental interactions and their implications for the Higgs hierarchy problem. We consider the framework of Strongly Interacting Light Higgs with partial compositeness. In generic models of partial compositeness, the existing constraints from $\mu \to e\gamma$ and the electric dipole moment (EDM) of the electron require the scale of Higgs compositeness to be above $\sim \mathcal{O}(100)$ TeV. These mass scales lie beyond the direct reach of the LHC and envisioned future colliders and are comparable to, or higher than, those accessible to future $\mu \to 3e$ and $\mu N\to eN$ searches. We show, however, that models where the strongly coupled sector has an accidental $U(3)\times \mathrm{C}\mathrm{P}$ or $U(2)\times U(1)\times \mathrm{C}\mathrm{P}$ symmetry, broken by the elementary–composite mixings, can substantially relax these constraints. In the $U(3)$ case, these symmetries (1) lead to an accidental alignment of the Yukawa and dipole couplings at leading order, suppressing $\mu \to e\gamma$ and the electron EDM, allowing the compositeness scale to lie in the few-TeV range; (2) are probed by the upcoming $\mu \to eee$ and $\mu N\to eN$ experiments; and (3) provide a direct target for current and future collider experiments. In the $U(2)\times U(1)$ case, $\mu \to e\gamma$ and the electron EDM remain important constraints, while upcoming searches for $\mu \to eee$, $\mu N\to eN$ and flavor-violating $\tau$ decays provide complementary probes. We discuss how these accidental symmetries can arise in the infrared compatibly with the dynamical generation of flavor hierarchies in the ultraviolet.