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

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