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Electron-to-Tau Lepton Flavor Violation at the Electron-Ion Collider

We analyze the potential sensitivity of a search for $e\rightarrowτ$ conversion at a proposed electron-ion collider (EIC) facility. To that end, we calculate the cross sections for $e\rightarrowτ$ events in a leptoquark framework assuming that the leptoquark masses are on the order of several hundred GeV or more. Given present limits on leptoquarks from direct searches at HERA and rare decay processes, an EIC sensitive to 0.1 fb $e\rightarrowτ$ cross sections could probe previously unexplored regions of parameter space for these lepton flavor violating events (assuming 90 GeV center-of-mass energy and 10 fb$^{-1}$ integrated luminosity). Depending on the species of leptoquark and flavor structure of the couplings, an EIC search could surpass the HERA and rare process sensitivity to $e\rightarrowτ$ conversion amplitudes by as much as an order of magnitude or more. We also derive updated limits on quark flavor-diagonal LFV leptoquark interactions using the most recent BaBar $τ\rightarrow eγ$ search. We find that limits from an EIC $e\rightarrowτ$ search could be competitive with the most recent $τ\rightarrow eγ$ limit for a subset of the quark flavor-diagonal leptoquark couplings. Using an SU(5) GUT model in which leptoquark couplings are constrained by the neutrino masses and mixing, we illustrate how observable leptoquark-induced $e\rightarrowτ$ conversion can be consistent with stringent LFV limits imposed by $μ\rightarrow eγ$ and $μ\rightarrow e$ conversion searches.