The weight for random quark masses

In theories in which the parameters of the low energy theory are not unique, perhaps having different values in different domains of the universe as is possible in some inflationary models, the fermion masses would be distributed with respect to some weight. In such a situation the specifics of the fermion masses do not have a unique explanation, yet the weight provides the visible remnant of the structure of the underlying theory. This paper introduces this concept of a weight for the distribution of masses and provides a quantitative estimate of it from the observed quarks and leptons. The weight favors light quark masses and appears roughly scale invariant (rho ~ 1/m). Some relevant issues, such as the running of the weight with scale and the possible effects of anthropic constraints, are also discussed.