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 ${\ensuremath{\mu}}^{2}$, which determines the weak interaction scale, is closer to the quantum chromodynamics scale than to the grand unification or Planck scales. We consider a novel approach to this problem, based upon the idea that ${\ensuremath{\mu}}^{2}$ takes different values in different domains of the Universe. The whole range of values for ${\ensuremath{\mu}}^{2}$, from ${+M}_{P}^{2}$ to ${\ensuremath{-}M}_{P}^{2}$, is explored, and it is found that only for values in a narrow window is life likely to be possible. The observed value of ${\ensuremath{\mu}}^{2}$ is fairly typical of the values in this window.