In theories in which different regions of the universe can have different values of certain physical parameters, we would naturally find ourselves in a region where they take values favorable for life. We explore the range of such viable values of the mass parameter in the Higgs potential, ${\mu }^2$. For ${\mu }^2<0\mathrm{}$, the requirement that complex elements be formed suggests that the Higgs vacuum expectation value $v$ must have a magnitude less than 5 times its observed value. For ${\mu }^2>0\mathrm{}$, baryon stability requires that $|\mu |\ll M_P$, the Planck mass. Smaller values of $|{\mu }^2|$ may or may not be allowed depending on issues of element synthesis and stellar evolution. We conclude that the observed value of ${\mu }^2$ appears reasonably typical of the viable range, and a multiple-domain scenario may provide a plausible explanation for the closeness of the QCD scale and the weak scale.

• Received 30 July 1997

DOI:https://doi.org/10.1103/PhysRevD.57.5480