2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/42739It is found that in the SM the Ward-Takahashi(WT) identities of the axial-vector currents and the charged vector currents of fermions are invalid after spontaneous symmetry breaking. The spin-0 components of Z and W fields are revealed from the invalidity of these WT identities. The masses of these spin-0 components are at $10^{14}$GeV. They are ghosts. Therefore, unitarity of the SM after spontaneous symmetry breaking is broken at $10^{14}$GeV.18 pagesHigh Energy Physics - Phenomenologytext