Understanding fine structure constants and three generations

Abstract

We put forward a model inspired by random dynamics that relates the smallness of the gauge coupling constants to the number of generations being “large”. The new element in the present version of our model is the appearance of a free parameter x that is a measure of the (presumably relatively minor) importance of a term in the plaquette action proportional to the trace in the (16,2,3) representation of the standard model. Calling Ngen the number of generations, the sets of allowed (Ngen, xNgen) -pairs obtained by imposing the three measured coupling constant values of the standard model form three lines. In addition to finding that these lines cross at a single point (as needed for a consistent fit), the intersection occurs with surprising accuracy at the integer Ngen=3 (thereby predicting exactly three generations). It is also encouraging that the parameter x turns out to be small and positive as expected.