Can a Higgs Field in an Isospin Triplet Give Mass to a Standard Model Quark?

[arivero]

Let me see if I get it right or I dreamed it: in order to give mass to a quark or a lepton the higgs field must be in the same isospin representation that the fermion, must it? IE, can a particle in a isospin triplet get mass from the minimal higgs? Or in the reverse, should a triplet higgs contribute to the mass of a standard model quark?

 

[BenTheMan]

arivero---

The only requirement is that you make a singlet under the gauge group out of the higgs and two fermions---this is the requirement that the Lagrangian be gauge invariant. I may be wrong, but isospin isn't what you should be thinking of. You should be thinking of standard model quantum numbers, i.e. SU(3)xSU(2)xU(1).

I wrote a rather long post on mass terms and the higgs that may answer some of your questions on another forum. I'll link to it here, but I don't know if linking to another forum is exactly kosher :)

http://www.sciforums.com/showthread.php?t=69369&highlight=higgs+gauge+invariance

 

[arivero]

Ah yes, I call isospin to the quantum numbers of the electroweak SU(2). Some old books name it "weak isospin" and I got hang of the name. Point is, given that the left fermion is a SU(2) doublet, are we forced to put the higgs field also in a SU(2) doublet or are there other solutions?