Weinberg on the anomaly

Does anybody have more details about the argument developed in
Weinberg, v II p 381-382 (around formula 22.3.39) where it is argued
that "the anomalies in a given set of symmetries therefore are
unaffected by the possible presence of fermions with a mass allowed by
these symmetries"?

Weinberg does not give bibliography for this part of the topic; any
pointer?

If I understand it well, it means that if for instance the top mass is
allowed by the fundamental symmetry group, then the top could not
contribute to anomalies in the fundamental theory and, by 't hooft
principle, it could not contribute neither to anomalies in effective
theories built upon the fundamental.

I wonder if I could then to conclude that mesons of the third family
are unaffected by the chiral anomaly.

Yours,

Alejandro

.

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