Higgs mechanism and relativity

[jbar18]

Hi all,

Having looked into the Higgs mechanism a bit (I am a physics undergrad, so my understanding is pretty basic if even correct), I have come up with a question. I understand that the way that the Higgs field gives mass to the W and Z bosons is different to the way that it gives leptons their mass, and the most accessible description of how leptons gain their mass is that the Higgs boson allows leptons to change their helicity. In the standard model, if leptons could not change their helicity, they would be massless. The Higgs boson essentially allows them to get away with changing their helicity, and the frequency with which they do this is related to their mass. The top quark supposedly flips its helicity very often, the electron not so much. That is my understanding so far anyway.

My question is this: When we change reference frame so that particles are moving very quickly, their mass appears to increase. I am wondering what implications this has for the Higgs mechanism - it would seem to imply that particles interact more heavily with the Higgs field if they are moving faster relative to you, but this sounds like nonsense for obvious reasons. I couldn't help but notice that there is no dependency of the other coupling constants on the choice of reference frame (charge is the same even if you move it quickly), but mass does appear to be dependent. Is the answer to this question known, and if so, is it insightful in any way?

My first thought is that the frequency of interaction of particles with the Higgs field would appear to increase due to time dilation, and if mass is proportional to this frequency, it would surely explain the phenomenon.

Thanks

 

[dauto]

You're confusing rest mass with relativistic mass. Rest mass does not depend on the reference frame and is indeed related to a coupling constant (Talking about fundamental fermions here). Relativistic mass is the one that depends on the movement of the particle and is just another name for energy. The concept of relativistic mass is redundant and hardly ever actually used (People use the word energy instead), it leads to more confusion than what it's worth and should, in my opinion, be entirely abolished from physics books.

 

[Bill_K]

In the standard model, if leptons could not change their helicity, they would be massless. The Higgs boson essentially allows them to get away with changing their helicity, and the frequency with which they do this is related to their mass. The top quark supposedly flips its helicity very often, the electron not so much. That is my understanding so far anyway.

The Higgs field contributes a term to the Hamiltonian that connects right-handed and left-handed fermions. But there is no "flipping" going on. The situation is time-independent.

Say you had a two-state system with a Hamiltonian
$$\left(\begin{array}{cc}E_1&V\\V&E_2\end{array}\right)$$
V connects state 1 with state 2. Would you say it is "causing the system to flip back and forth between state 1 and state 2"?? I hope not! You should diagonalize the Hamiltonian and look at the eigenstates. The correct statement is that V causes the eigenstates to be time-independent superpositions of state 1 with state 2. Likewise the eigenstates of a fermion, in which the eigenstates are mixtures of right- and left-handedness.

 

[michael879]

I think you're also confusing helicity with chirality. The two are only the same for massless particles

 

[jbar18]

Thanks for clearing that up, I had gotten confused as you say. Also I think I meant to say "Higgs condensate particles" at one point, not "Higgs bosons" (are they the same?). Other than that, is the rest of my understanding correct?

 

[jbar18]

The Higgs field contributes a term to the Hamiltonian that connects right-handed and left-handed fermions. But there is no "flipping" going on. The situation is time-independent.

Say you had a two-state system with a Hamiltonian
$$\left(\begin{array}{cc}E_1&V\\V&E_2\end{array}\right)$$
V connects state 1 with state 2. Would you say it is "causing the system to flip back and forth between state 1 and state 2"?? I hope not! You should diagonalize the Hamiltonian and look at the eigenstates. The correct statement is that V causes the eigenstates to be time-independent superpositions of state 1 with state 2. Likewise the eigenstates of a fermion, in which the eigenstates are mixtures of right- and left-handedness.

Yes, I wrote it in very basic (and incorrect) terms because that is pretty much the only way I've seen it written.

I think you're also confusing helicity with chirality. The two are only the same for massless particles

Also correct. Apologies.

 

[michael879]

Actually I retract my comment. You were talking about the fields before the gauge fixing that gives them mass, so technically helicity and chirality would be the same. However, I think part of your confusing is from thinking of chirality as a vector, rather than an intrinsic property