In two Higgs doublet model (2HDM), how the W and Z bosons get mass? I am specifically looking for Type II 2HDM case.
Two complex SU(2) doublets contain eight real fields. Three of which are absorbed in the usual way to make w+/- and Z boson massive. Five degrees of freedom are kept free. They are five physical Higgs fields of this theory. They can be counted as one charged scalar, two neutral scalars and one pseudo scalar Higgs fields.
Thank you very much sir for the answer, there is one more thing I want to ask: how to define the physical Higgs (SM-like) in this model?
A physical Higgs is the one which can be detected by experiments. Standard model Higgs is neutral; remember it was so difficult to detect it ! Your model has two neutral scalars. Perhaps the one with lower mass can be identified with the standard model Higgs. But this is not an entirely correct assumption. In case the lighter one has escaped detection (it depends on the details of the model parameters), you are seeing the heavier one.
Perhaps one should view it as, experiments have seen a Higgs boson at 125.09 GeV, which is the theoretical expectation from the study of SM.
ref: http://pdg.lbl.gov/2016/reviews/rpp2016-rev-higgs-boson.pdf
Basabendu, in regards to your second question: The 2HDM has for sure more free parameters than the pure SM, then, you can fix the M_h=125 GeV of the SM-like Higgs boson in a set of values of parameter space. It will depend of the 2HDM you take, sometimes the set is softly or hardly constrained.
Thank you Daniel for your input. But my question is not exactly regarding the mass-scale of the Higgs, what I am looking for is the presentation of the physical Higgs when there are two fields (say \Phi_1 and \Phi_2) under consideration.
Basabendu, take φ10 and φ20 which are two neutral members of φ1 and φ2. They will invariably mix with each other at electroweak scale because there is no other quantum number which will distinguish between them. Then form combinations cos α φ10+ sin α φ20 and -sin α φ10 + cos α φ20. You will get an expression for the mixing angle α in terms of model parameters from the minimization conditions of Higgs potential.
In the Higgs potential, after substituting appropriate VEVs (for simplicity take them real) of two Higgs doublets, among other terms, you should obtain, (φ10)2, (φ20)2 as well as φ10φ20 terms with appropriate coefficients, which will form a 2x2 mass matrix in (φ10, φ20) basis. Upon diagonalization this matrix yields the mixing angle α in terms of model parameters. New basis obtained after diagonalization is actually the mass basis which you are seeking.
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