Exploring lepton flavor violation phenomena of the Z and Higgs bosons at electron-proton colliders

We conduct a comprehensive analysis of the potential for discovering lepton flavor violation (LFV) phenomena associated with the Z and Higgs bosons at the LHeC and FCC-he. Our thorough investigation highlights the exceptional suitability of electron-proton colliders for probing these rare new physics signals, due to their distinct advantages, such as negligible pileups, minimal QCD backgrounds, electron-beam polarization P-e, and the ability to distinguish charged-current from neutral-current processes. In our analysis of LFV of the Z boson, we employ an innovative indirect probe, utilizing the t-channel mediation of the Z boson in the process pe(-)-> j tau(-). For LFV in the Higgs sector, we examine direct observations of the on-shell decays of H -> e(+)tau(-) and H ->mu(+/-)tau(-/+) through the charged-current production of H. Focusing on H -> e(+)tau(-) is highly efficient due to the absence of positron-related backgrounds in the charged-current modes at electron-proton colliders. Through a dedicated signal-to-background analysis using the boosted decision tree algorithm, we show that the LHeC with a total integrated luminosity of 1 ab-1 can establish significantly lower 2 sigma bounds than the HL-LHC with 3 ab(-1). Specifically, we find Br(Z -> e tau)<2.2x10(-7), Br(H -> e tau)<1.7x10(-4), and Br(H ->mu tau)<1.0x10(-4) when we apply the optimal cut on the boosted decision tree output. Furthermore, our study reveals the exceptional precision of the FCC-he in measuring the LFV signatures of the Z and Higgs bosons, indicating a promising potential for future discoveries in this fascinating field.