Leptoquark-induced CLFV decays with a light SM-singlet scalar

The Standard Model (SM), if augmented with a light SM-singlet scalar $\phi$ and a TeV-scale scalar leptoquark (LQ) $S_1$, 2-body charged lepton flavor violating (CLFV) decay channels can be accessed with $\phi$ as one of the final states, where the leading order effective interactions between $\phi$ and the SM fields arise at one-loop level. Further, in the presence of $S_1$, $\phi$ can mediate 3-body CLFV processes with either two photons or two gluons in the final states. Thus, the model predicts an exotic 3-body CLFV channel: $\ell_A\to\ell_B gg$, which can be tested/constrained only through some future high-energy experiments looking for di-gluon signals from a leptonic decay.