In the Standard Model (SM), there is no constrain for how many
generations of quarks should or could have.
In a recent article “Three
Generations in Minimally Extended Standard Models, http://arxiv.org/abs/1205.4483 (written
by Paul Frampton, Chiu Man Ho and Thomas W. Kephart)”, it stated that all anomalies
in the Standard Model can be canceled if there are three and only three generations.
They can find infinitely many models that cancel all gauge anomalies, but all
of these new models require three generations.
However, this new discovery was published in the book “Super
Unified Theory” (ISBN 0-916713-02-4, Copyright # TX 1-323-231, Library of
Congress Catalog Card Number 84-90325) long ago, and the brief discussion of this
issue is also available in the article “48, the exact number for the number of
elementary particles, http://prebabel.blogspot.com/2012/04/48-exact-number-for-number-of.html
”.
In fact, in Super Unified Theory (Axiomatic Physics), the
three and only three generations are the absolute, way beyond as a requirement
for cancelling the anomalies.
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