Search for Lepton Flavor Violating Signals at the Future Electron-Proton Colliders

The search for lepton flavor violation (LFV) is a powerful probe to look for new physics beyond the Standard Model. We explored the possibility of searches for LFV $Z$ boson couplings to electron and muon pairs at the upcoming electron-proton colliders, namely the Large Hadron Electron Collider (LHeC) and the Future Circular lepton-hadron Collider (FCC-eh). We employed the study via a single muon plus an associated jet channel to search for the LFV signal. We used a multivariate technique to obtain an improved signal-background analysis. By using the condition on nonobservation of any significant deviation of the signal over the expected background, we provide an upper limit on the LFV $Z$ boson coupling and corresponding branching ratio (BR). We find that an upper limit of up to $1.13\times {10}^{-7}$ and $4.64\times {10}^{-8}$ can be set on BR($Z\to e\mu$) at 95% confidence level (C.L.) with one year run of LHeC and FCC-eh, respectively, if the LFV coupling is governed by vector or axial-vector coupling. For tensor or axial-tensor coupling, these limits can be improved up to $2.34\times {10}^{-8}$ and $5.02\times {10}^{-9}$ for LHeC and FCC-eh machines, respectively, at 95% C.L. The projected numbers improve significantly over the existing limit of $2.62\times {10}^{-7}$ set by ATLAS.