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We present a case study for the doubly charged Higgs bosons $H^{\pm\pm}$ pairproduction in $e^+e^-$ and $pp$ colliders with their subsequent decays to fourcharged leptons. We consider the Higgs Triplet Model (HTM) not restricted bythe custodial symmetry and the Minimal Left-Right Symmetric Model (MLRSM). Themodels include scalar triplets with different complexity of scalar potentialsand, due to experimental restrictions, completely different scales ofnon-standard triplet vacuum expectation values. In both models, a doublycharged Higgs boson $H^{\pm\pm}$ can acquire a mass of hundreds ofgigaelectronvolts, which can be probed at HL-LHC, future $e^+e^-$, and hadroncolliders. We take into account a comprehensive set of constraints on theparameters of both models coming from neutrino oscillations, LHC, $e^+e^-$ andlow-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 leptonand hadron colliders is comparable in both models, though more pronounced inMLRSM. We show that the decay branching ratios can be different within bothmodels, leading to distinguishable four lepton signals and that the strongestare $4\mu$ events yielded by MLRSM. Typically we find that MLRSM signals areone order of magnitude larger that in HTM. For example, the $pp \to 4\mu$ MLRSMsignal for 1 TeV $H^{\pm \pm}$ mass results in a clearly detectablesignificance of $S \simeq 11$ for HL-LHC and $S \simeq 290$ for FCC-hh. Finallywe provide quantitative predictions for the dilepton invariant massdistributions and lepton separations which help to identify non-standardsignals.

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