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

Abstract

We comprehensively study the potential for discovering lepton flavor violation (LFV) phenomena associated with the $Z$ and Higgs bosons at the LHeC and FCC-he. Our meticulous investigation reveals the remarkable suitability of electron-proton colliders for probing these rare new physics signals. This is due to the distinct advantages they offer, including negligible pileups, minimal QCD backgrounds, electron-beam polarization $P_e$, and the capability of distinguishing the charged-current from neutral-current processes. In our pursuit of LFV of the $Z$ boson, we employ an innovative indirect probe, utilizing the $t$-channel mediation of the $Z$ boson in the process $p{e}^{-}\to j{\tau }^{-}$. For LFV in the Higgs sector, we scrutinize direct observations of the on-shell decays of $H\to e^{+}{\tau }^{-}$ and $H\to {\mu }^{\pm }{\tau }^{\mp }$ through the charged-current production of $H$. Focusing on $H\to e^{+}{\tau }^{-}$ proves 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 with the boosted decision tree algorithm, we demonstrate that the LHeC with the total integrated luminosity of $1{\mathrm{ab}}^{-1}$ can put significantly lower $2\sigma$ bounds than the HL-LHC with $3{\mathrm{ab}}^{-1}$. Specifically, we find $\mathrm{Br}(Z\to e\tau )<2.2\times 10^{-7}$, $\mathrm{Br}(H\to e\tau )<1.7\times 10^{-4}$, and $\mathrm{Br}(H\to \mu \tau )<1.0\times 10^{-4}$. Furthermore, our study uncovers the exceptional precision of the FCC-he in measuring the LFV signatures of the $Z$ and Higgs bosons, which indicates the potential for future discoveries in this captivating field.

Comments: Extensive updates including the BDT analysis for the LFV Z, the distinction between the LFV Z and LHV Z', and the signal significance when the number of backgrounds approach 0