Re: Why is the Higgs Boson tachyonic?
- From: Darth Sidious <sidious.lord@xxxxxxxxx>
- Date: Thu, 30 Mar 2006 03:45:57 +0000 (UTC)
The Higgs boson is *not* tachyonic. The field \Phi which has a
potential like a mexican hat is *not* the Higgs field. You get
the Higgs field by choosing a gauge and a vacuum for your
action, developping the action in the neighbourhood of that
vacuum.
Then you get massless Goldstone bosons which get `eaten' by
the vector bosons in order to get the right number of degrees
of freedom for a massive particle (three for spin one). The Higgs
boson is the massive scalar that rests after after taking out the
Goldstone bosons. The coupling of the vector bosons to the
Higgs field is something like an effective mass term.
As the vacuum you chose is stable, the Higgs's mass squared
is positive. You should look this up. It's in all serious textbooks
on QFT.
{This is all about the `bare' Higgs mass. Of course, the real
observable mass gets radiative corrections but in the end the
mass squared is positive as it should.}
.
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