Invalid Ward-Takahashi identities and broken unitarity of the SM
Abstract
It 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 1014GeV. They are ghosts. Therefore, unitarity of the SM after spontaneous symmetry breaking is broken at 1014GeV.
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