Bounds on 2HD potential

  • Thread starter Safinaz
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  • #1
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Hi all,

I found that any two Higgs doublets potential should be bounded from below - at ## V \to - \infty ##. I want to know why this bound is assumed or what does it mean ?

Also are there any textbooks to learn how to make this bound on any other general potential and so to constrain the potential's parameters ?

Best.
 

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  • #2
Orodruin
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If the potential is not bounded from below, your theory has no ground state.
 
  • #3
ChrisVer
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The bounds are obtained just by looking at the potential...
For example [itex]V=a |\phi|^2 [/itex] is bounded for [itex]a>0[/itex] and unbound for [itex]a<0[/itex]. If you draw the potential you will see that.
In case you have more than one fields, I guess one has to look at each direction independently ... So the potential for two Higgses could be described by a sheet [itex]V(\phi_1, \phi_2)[/itex] on the space of [itex]\phi_1, \phi_2[/itex], if it's bounded it means that it can't go to [itex]-\infty[/itex] anywhere.

If there was no bound then even if you had a vacuum at some potential's minimum, this vacuum would not be stable. At some point the field would "escape" the well, and then start rolling down forever.
 

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