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arxiv: 1607.01618 · v5 · pith:MIIFOQ7Ynew · submitted 2016-07-05 · ✦ hep-ph · hep-th

The spin-charge-family theory offers understanding of the triangle anomalies cancellation in the standard model

classification ✦ hep-ph hep-th
keywords trianglecancellationmodelstandardanomaliesanomalyanti-fermionsfermions
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The standard model has for massless quarks and leptons "miraculously" no triangle anomalies due to the fact that the sum of all possible traces $Tr [\tau^{Ai}$$ \tau^{Bj}$$ \tau^{Ck}]$ --- where $\tau^{Ai}, \tau^{Bi}$ and $\tau^{Ck}$ are the generators of one, of two or of three of the groups $SU(3), SU(2)$ and $U(1)$ --- over the representations of one family of the left handed fermions and anti-fermions (and separately of the right handed fermions and anti-fermions), contributing to the triangle currents, is equal to zero. It is demonstrated in this paper that this cancellation of the standard model triangle anomaly follows straightforwardly if the $SO(3,1), SU(2), U(1)$ and $ SU(3)$ are the subgroups of the orthogonal group $SO(13,1)$, as it is in the spin-charge-family theory. We comment on the $SO(10)$ anomaly cancellation, which works if handedness and charges are related "by hand".

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