Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking

Abstract

One of the puzzles of the Standard Model is why the mass parameter which determines the scale of the Weak interactions is closer to the scale of QCD than to the Grand Unification or Planck scales. We discuss a novel approach to this problem which is possible in theories in which different regions of the universe can have different values of the physical parameters. In such a situation, we would naturally find ourselves in a region which has parameters favorable for life. We explore the whole range of values of the mass parameter in the Higgs potential, $\mu^2$, from $+M_P^2$ to $-M_P^2$ and find that there is only a narrow window, overlapping with the observed value, in which life is likely to be possible. The observed value of $\mu^2$ is fairly typical of the values in this range. Thus multiple domain theories in which $\mu^2$ varies among domains may give a promising approach to solving the fine tunign problem and explaining the closeness of the QCD scale and the Weak scale.