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There is a 2HDM that predicts 3 neutral and 2 charged Higgs particles.

There are also many more models out there. I already did some searching, but there is a large body of work here, and various models.

Is there any Higgs model that would result in 5 Higgs, where one is neutral and four are charged?

Optionally, two of the charged Higgs will have spin, and the other 2 will have opposite spin.

It would look something like this:

Charge Spin
0      0
+      1
-      1
+      2
-      2
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I think it's impossible, because you'd break electromagnetism if the spectrum had a single neutral Higgs in a 2HDM.

I presume both doublets obtain VEVs such that 8 real dof are supposed to be reduced to 5 dof after EWSB, with 3 dof eaten by massive gauge bosons.

But if the Higgs doublets have a single neutral component, one of the charged ones must be VEVed, breaking EM, and actually giving only 4 Higgs bosons, a massive photon and broken EM.

As for your remarks about spin, you may be slightly confused. The Higgses are always spin-0 scalars. They cannot change spin by EWSB or anything else. The scenarios you describe are impossible.

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  • $\begingroup$ I've written this quickly on my tablet, I might think about it a bit more to make sure $\endgroup$
    – innisfree
    Commented Jan 17, 2016 at 11:14
  • $\begingroup$ The SM says there is a single neutral Higgs, so does your first statement apply only for the 5 Higgs case? $\endgroup$
    – BAR
    Commented Jan 17, 2016 at 11:16
  • $\begingroup$ @bar thanks, yes, it only applied to 2hdm (and thus not the SM) $\endgroup$
    – innisfree
    Commented Jan 17, 2016 at 11:23

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