Searching for Lepton Flavor Violating decays of the Higgs Boson into μτ, eτ, and eμ final states at FCC-ee

We investigate the projected sensitivity of the FCC-ee in probing the LFV decay of the 125 GeV Higgs boson, $h\to\mu\tau$, $h\to e\tau$, and $h \to e\mu$ at center-of-mass energy of 240 GeV with an integrated luminosity of 5 ab$^{-1}$. With the clean multi-lepton final states, we consider the Higgs production modes that contribute to $e^+e^- \to \ell\ell h$, in particular, the Higgs-strahlung and the vector boson fusion production channels. The 95\% CL upper limits on branching ratio are found to be $5.92 \times 10^{-4}$, $6.27 \times 10^{-4}$, and $7.48 \times 10^{-5}$ for the channels $h\to\mu\tau$, $h\to e\tau$, and $h \to e\mu$, respectively. In addition, we also consider the LFV decay of a new CP-even Higgs boson with mass in the range of $110-200$ GeV. The projected FCC-ee sensitivities are then compared to those from low energy searches for $\ell\to\ell'\gamma$ decay. We find that the FCC-ee sensitivity for the LFV decays of the Higgs in the $e-\tau$ and $\mu-\tau$ channels is superior to the low-energy constraints. However, in the $e-\mu$ case, the low energy search offers stronger constraints.