Probing a 146 GeV cLFV scalar using the LHC and low-energy experiments

The CMS Collaboration reported a local excess at $146~\mathrm{GeV}$ in the search for the lepton-flavor-violating decay of the Higgs boson and additional Higgs bosons in the $e\mu$ final state at $\sqrt{s}= 13~\mathrm{TeV}$. If confirmed, this would constitute a major piece of evidence of charged lepton flavor violation (cLFV). We investigate the compatibility of the claimed signal with the full suite of existing low-energy cLFV constraints in a bottom-up effective description: a single real scalar of mass $146~\mathrm{GeV}$ coupled to gluons and to all charged-lepton bilinears, with seven free parameters that simultaneously control the LHC production cross section, every di-lepton decay channel, and every low-energy cLFV observable. A Bayesian MCMC analysis against $\mu-e$ conversion, muonium-antimuonium oscillation, three-lepton and radiative LFV decays, semileptonic $\tau$ LFV decays, and LHC di-lepton searches yields a preferred mode with peaked value $Y_{e\mu} \sim 10^{-4.09}$, already cut into by the current $\mu-e$ conversion limits. The projected sensitivities of Mu2e, COMET, Mu3e, MACE, MEG~II, Belle~II, STCF, and the HL-LHC directly probe the region of coupling space selected by the CMS excess, so the complementarity between high-energy and low-energy cLFV probes will either corroborate or decisively exclude the scalar interpretation of the anomaly within the next decade.