Single Production of Doubly Charged Higgs at Muon Collider

In this paper, we study the single production of doubly charged Higgs $H^{\pm \pm }$ in the type-II seesaw at the high energy muon collider. Compared with the pair production channel ${\mu }^{+}{\mu }^{-}\to H^{++}{H}^{--}$, the single production channel ${\mu }^{+}{\mu }^{-}\to {\mu }^{\mp }{\mathrm{\ell }}^{\mp }{H}^{\pm \pm }$ in principle could probe the mass region above the threshold $m_{H^{\pm \pm }}>\sqrt{s}\mathrm{/}2$. The single production channel depends on the Yukawa coupling $h$, which is related to the neutrino oscillation parameters. We show that the Majorana phases ${\phi }_1$ and ${\phi }_2$ have great impact on the individual cross section of the single production. We find that the same sign dilepton signature from $H^{\pm \pm }\to {\mathrm{\ell }}^{\pm }{\mathrm{\ell }}^{\pm }$ could probe $m_{H^{\pm \pm }}\lesssim 2.6(7.1)$ TeV at the 3 (10) TeV muon collider when the triplet VEV $v_{\mathrm{\Delta }}\lesssim 3$ eV.