Scalar fields and the Higgs boson

[HeavyWater]

This is more of a QFT question, so the moderator may want to move it to another forum.

The simplest example of a QFT that I learned was the scalar field; in Sakurai's 1967 textbook.
I know the Higgs is a J=0 particle. Is it described by the simple scalar field discussed in Sakurai's text? I ask because I hear about the complexity of the Higgs and that there may be up to 5 Higgs bosons.

Your thoughts and comments are welcome.

 

[Avodyne]

Yes, if we write the fields of the Standard Model that correspond to particles of definite mass. Then there is a real scalar field that corresponds to the physical Higgs boson.

However, if instead we use fields that have definite transformation properties under the gauge symmetries, then the Higgs field is a complex doublet of the SU(2) gauge symmetry (and also transforms under the U(1) hypercharge symmetry); that is, two complex scalar fields, equivalent to four real scalar fields. After spontaneous symmetry breaking, three of these fields end up as the longitudinal components of the massive $W^\pm$ and $Z^0$ gauge fields, and the fourth is the field corresponding to the Higgs particle.

In some extensions of the Standard Model, there are two Higgs doublets, equivalent to 8 real scalar fields. 3 of these end up as the longitudinal $W^\pm$ and $Z^0$, and the remaining 5 are scalar bosons. Three have electric charge zero, and the other two have electric charge $\pm1$ (in units of the electron charge).

 

[HeavyWater]

Thank you Avodyne. You answered my question and anticipated my next question. It's going to take me a while to digest this information. It is very helpful. Thank you.