Lepton flavor violating signals driven by CP symmetry of order 4

Abstract

CP4 3HDM is a curious version of the three-Higgs-doublet model built upon a CP symmetry of order 4 (dubbed CP4). When extended to fermions, CP4 leads to unusually tight correlations between the scalar and Yukawa sectors and induces tree-level flavor changing neutral couplings. Still, viable scenarios exist, in which quark flavor changing signals remain within experimental limits. In this work, we extend CP4 to the lepton sector and investigate whether the lepton-Higgs couplings and lepton flavor violating (LFV) signals can also be kept under control. We consider two classes of LFV processes: tree-level leptonic decays of the 125 GeV Higgs boson and the muon decays $\mu\to e\gamma$ and $\mu \to 3e$. For each CP4-invariant lepton Yukawa scenario, we perform a focused Yukawa sector scan that uses physical lepton properties as input and suppresses LFV effects. We identify a promising CP4 3HDM scenario compatible with the present-day experimental constraints, show that it can accommodate the recent CMS hint of a 146 GeV scalar decaying to $e\mu$, and argue that this interpretation can be tested at future colliders through the search of comparably strong $ee$ and $\mu\mu$ signals.