Anthropic Argument for Three Generations

Abstract

The standard model of particle physics contains N_gen=3 generations of quarks and leptons, i.e., two sets of three particles in each sector, with the two sets differing by 1 unit of charge in each. All 12 "predicted" particles are now experimentally accounted for, and there are strong (though not air-tight) arguments that there are no more than three generations. The question is: why exactly N_gen=3? I argue that three generations is a natural prediction of the multiverse theory, provided one adds the additional, quite reasonable assumption that N_gen in a randomly realized universe is a steeply falling function of number. In this case N_gen > 2 to permit CP violation (and so baryogenesis and thus physicists) and N_gen < 4 to avoid highly improbable outcomes. I thereby make a testable anthropic-principle prediction: that when a theory of randomly realized N_gen is developed, the probability will turn out to be steeply falling in N_gen.