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Is it a coincidence that the mass of the Higgs boson is exactly half the electroweak energy scale?

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    $\begingroup$ Hi Maura, and welcome to Physics Stack Exchange! We prefer that each separate question should be asked on its own, so I removed the extra thing you were asking about the Higgs and its antiparticle. Feel free to post that as a separate question (if it hasn't been asked on the site already). $\endgroup$ – David Z Mar 25 '13 at 19:05
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It's not exactly half. The physical Higgs mass is something around 125 or 126 GeV, but the EW scale is a little less than twice that.

There is a relationship of sorts between the two values, though: the Higgs field $\phi$ is subject to a potential of the form

$$V(\phi) = \mu^2\lvert\phi\rvert^2 + \lambda\lvert\phi\rvert^4$$

Given this potential, the bare mass of the Higgs boson will be $\mu$ and the electroweak energy scale is $\sqrt{-\frac{\mu^2}{\lambda}}$. The relationship depends on the constant $\lambda$.

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