Search for doubly charged Higgs bosons through VBF at the LHC, and beyond

Production and decays of doubly charged Higgs bosons at the LHC and future hadron colliders triggered by vector boson fusion mechanism are discussed in the context of the Minimal Left-Right Symmetric Model. Our analysis is based on the Higgs boson mass spectrum compatible with available constraints which include FCNC effects and vacuum stability of the scalar potential. Though the parity breaking scale $v_R$ is large ($\sim$ few TeV) and scalar masses which contribute to FCNC effects are even larger, consistent Higgs boson mass spectrum still allows us to keep doubly charged scalar masses below 1 TeV which is an interesting situation for LHC and future FCC colliders. We have shown that allowed Higgs bosons mass spectrum constrains the splittings ($M_{H_{1}^{\pm \pm}}-M_{H_{1}^\pm}$), closing the possibility of $H_{1}^{\pm\pm}\to W_{1}^\pm H_{1}^\pm$ decays. Assuming that doubly charged Higgs bosons decay predominantly into a pair of same sign charged leptons through the process $p p \rightarrow H_{1/2}^{\pm \pm} H_{1/2}^{\mp \mp} j j \rightarrow \ell^{\pm} \ell^{\pm} \ell^{\mp} \ell^{\mp} jj$, we find that for LHC operating at $\sqrt{s}=14$ TeV with an integrated luminosity at the level of $3000\,\mathrm{fb}^{-1}$ (HL-LHC) there is practically no chance to detect such particles at the reasonable significance level through this channel. However, 33 TeV HE-LHC and (or) 100 TeV FCC-hh open up a wide region for doubly charged Higgs boson mass spectrum to be explored. In FCC-hh, doubly charged Higgs bosons mass up to 1 TeV can be probed easily.