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Invalid Ward-Takahashi identities and broken unitarity of the SM

Bing An Li
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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 $10^{14}$GeV. They are ghosts. Therefore, unitarity of the SM after spontaneous symmetry breaking is broken at $10^{14}$GeV.

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Bing An Li. 2003-08-06. Invalid Ward-Takahashi identities and broken unitarity of the SM. https://arxiv.org/abs/hep-ph/0308071

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