Search of the heavy neutral Higgs boson H of the $U(1)_{B-L}$ model at the future multi-TeV $\mu^+\mu^-$ collider

The possible detection of a heavy neutral Higgs boson $H$ predicted by the $U(1)_{B-L}$ model at the future multi-TeV muon collider for the center-of-mass energies of $\sqrt{s} = 3, 6, 10, 30, 50$ TeV with integrated luminosities of ${\cal L}_{\rm con} = 1, 2, 3, 4, 10$ ${\rm ab^{-1}}$ and $\sqrt{s}=30, 50$ TeV, ${\cal L}_{\rm opt}=90, 250$ $\rm ab^{-1}$, are investigated. The following production and decay channels of the heavy Higgs boson through the Vector Boson Fusion (VBF) are considered: $\mu^+\mu^- \to \nu_\mu \bar\nu_\mu H \to \nu_\mu \bar\nu_\mu W^\pm W^\mp$ with the subsequent decay of the Higgs boson $H$ to pairs of $W^\pm W^\mp$ bosons. We show that promising signals with good statistical significances can be obtained in di-vector bosons channel, with $\nu_\mu \bar\nu_\mu \nu_ll^\pm \bar\nu_ll^\mp$ final states.