Discriminating the HTM and MLRSM models in collider studies via doubly charged Higgs boson pair production and the subsequent leptonic decays

Abstract: We present a case study for the doubly charged Higgs bosons $H^{\pm\pm}$ pair production in $e^+e^-$ and $pp$ colliders with their subsequent decays to four charged leptons. We consider the Higgs Triplet Model (HTM) not restricted by the custodial symmetry and the Minimal Left-Right Symmetric Model (MLRSM). The models include scalar triplets with different complexity of scalar potentials and, due to experimental restrictions, completely different scales of non-standard triplet vacuum expectation values. In both models, a doubly charged Higgs boson $H^{\pm\pm}$ can acquire a mass of hundreds of gigaelectronvolts, which can be probed at HL-LHC, future $e^+e^-$, and hadron colliders. We take into account a comprehensive set of constraints on the parameters of both models coming from neutrino oscillations, LHC, $e^+e^-$ and low-energy lepton flavour violating data and assume the same mass of $H^{\pm\pm}$. Our finding is that the $H^{\pm\pm}$ pair production in lepton and hadron colliders is comparable in both models, though more pronounced in MLRSM. We show that the decay branching ratios can be different within both models, leading to distinguishable four lepton signals and that the strongest are $4\mu$ events yielded by MLRSM. Typically we find that MLRSM signals are one order of magnitude larger that in HTM. For example, the $pp \to 4\mu$ MLRSM signal for 1 TeV $H^{\pm \pm}$ mass results in a clearly detectable significance of $S \simeq 11$ for HL-LHC and $S \simeq 290$ for FCC-hh. Finally we provide quantitative predictions for the dilepton invariant mass distributions and lepton separations which help to identify non-standard signals.