Probing flavor-diagonal couplings of doubly-charged scalar at low and high energies

We investigate the phenomenology of a TeV-scale doubly-charged scalar from the right-handed sector within the framework of left-right symmetric models. Focusing on its flavor-diagonal couplings to right-handed electrons and muons, we assess probes from both high-energy colliders and low-energy precision experiments. High-energy processes include Bhabha scattering at LEP and future circular electron-positron colliders (CEPC/FCC-ee), direct production at the LHC, and dedicated searches and precision measurements at proposed muon colliders and $\mu$TRISTAN. Low-energy observables encompass parity-violating M{\o}ller scattering, muon anomalous magnetic moment, and muonium-antimuonium oscillations. Our combined analysis indicates that for a doubly-charged scalar in the $1$-$3$ TeV range, the flavor-diagonal Yukawa couplings to electrons and muons as small as $10^{-2}$ are accessible. Observations of such a doubly-charged scalar would potentially point toward the type-I seesaw mechanism of neutrino masses in the left-right symmetric model with $D$-parity breaking.