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

In summary, the requirement for giving mass to a quark or lepton is that the higgs field must be in the same isospin representation as the fermion. This means that the Lagrangian must be gauge invariant. Isospin is not the correct way to think about this, rather it is the standard model quantum numbers (SU(3)xSU(2)xU(1)). The higgs field must be in a SU(2) doublet in order to give mass to the left fermion, but there may be other solutions.
  • #1
arivero
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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?
 
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  • #2
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
 
  • #3
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?
 

1. What is the Higgs boson and how does it relate to fermion masses?

The Higgs boson is a subatomic particle that was predicted by the Standard Model of particle physics. It is responsible for giving particles, including fermions, their mass through the Higgs mechanism. This mechanism involves the Higgs field, which permeates the entire universe, and interacts with particles to give them mass.

2. How was the Higgs boson discovered and what does it mean for our understanding of the universe?

The Higgs boson was discovered in 2012 by the Large Hadron Collider (LHC) at CERN. Its discovery confirmed the existence of the Higgs field and the Higgs mechanism, which is a crucial component of the Standard Model. This discovery has furthered our understanding of the fundamental building blocks of the universe and how they interact.

3. Why is it important to study the masses of fermions?

Fermions are one of the two fundamental classes of particles in the Standard Model and make up matter as we know it. Understanding their masses is crucial for understanding the fundamental forces and interactions that govern the behavior of matter. Additionally, the mass of fermions can also provide insights into the properties of the Higgs field and other fundamental particles.

4. How are the masses of fermions determined?

The masses of fermions are determined through experiments, such as the Large Hadron Collider, where scientists study the interactions of particles. The Higgs boson and other particles play a crucial role in these interactions, and the data collected from these experiments can be used to calculate the masses of fermions.

5. Are there any theories beyond the Standard Model that offer alternative explanations for Higgs and fermion masses?

Yes, there are several theories beyond the Standard Model that offer alternative explanations for Higgs and fermion masses. These include supersymmetry, extra dimensions, and composite models. These theories are still being actively researched and studied, and their potential implications for our understanding of the universe are being explored.

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