Higgs mediated CLFV processes $μN(eN)\rightarrowτX$ via gluon operators
We revisit charged lepton flavor violating (CLFV) scattering processes $\ell_{i} N \to τX \, (\ell_{i} \ni e, μ)$ mediated by Higgs. We point out that a new subprocess $\ell_{i} g \to τg$ via the effective interactions of Higgs and gluon gives the dominant contribution to $\ell_{i} N \to τX$ for an incident beam energy of $E_{\ell} \lesssim 1\,\text{TeV}$ in fixed target experiments. Furthermore, in the light of quark number conservation, we consider quark pair-production processes $\ell_{i} g \to τq \bar{q}$ ($q$ denotes quarks) instead of $\ell_{i} q \to τq$. This corrects the threshold energy of each subprocess contributing to $σ(\ell_{i} N \to τX)$. Reevaluation of $σ(\ell_{i} N \to τX)$ including all of relevant subprocesses shows that the search for $\ell_{i} N \to τX$ could serve a complementary opportunity with other relevant processes to shed light on the Higgs CLFV.