Statistical analysis of quark and lepton masses

Abstract

We study the hypothesis that new, approximately conserved chiral charges are mainly responsible for the observed quark and lepton mass ratios. A Monte Carlo calculation is described, which assigns different values of these chiral charges to the bare left- and right-handed components of a family of fundamental fermions of a given eletric charge and then calculates the fermion mass ratios. The distance between left- and right-handed components in chiral charge space is taken as a measure of the strength of the symmetry- breaking interaction which generates the corresponding mass matrix element. Our main prediction is the ratio of logarithms of mass ratios for successive members of a family of fermions. For the three lowest-mass members of a family, this ratio is found to be remarkably independent of the assumed number of fermions and of chiral charges and is in good agreement with experiments. Fluctuations between different families are predicted to be larger than those observed between leptons and quarks, which we take as evidence for some unifying interaction. Unification is also suggested by the failure of our model to reproduce the observed weak coupling matrix. We obtain estimates of the top-quark mass with big uncertainties and averages in the range from 6 to 30 GeV. The most likely order of magnitude of a presumed fourth-generation mass is 28 −12 +3 GeV. Neutrino masses are also discussed.