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The anthropic principle and the mass scale of the Standard Model
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The anthropic principle and the mass scale of the Standard Model
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In theories in which different regions of the universe can have different values of the the physical parameters, we would naturally find ourselves in a region which has parameters favorable for life. We explore the range of anthropically allowed values of the mass parameter in the Higgs potential, $\mu^2$. For $\mu^2<0$, 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 $\mu^2>0$, baryon stability requires that $|\mu|<<M_P$, 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 $\mu^2$ is reasonably typical of the anthropically allowed range, and that anthropic arguments provide a plausible explanation for the closeness of the QCD scale and the weak scale.
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