B What is source of fundamental particle charge?

[Berbit]

Hello,
Analogous to mass of fundamental (not composite) particles coming from interaction of those particles with the Higg's Field,
does charge of fundamental particles come from interaction of those particles with some known/hypothesized fundamental field?
Thank you!

 

[Drakkith]

I don't think so. I think it's an inherent property of the particle and isn't modeled as being caused by any sort of interaction.

 

[Orodruin]

The charge of a particle by definition is its fundamental interaction strength with the photon field. This is a property of the particle itself and not the result of any other field (as far as we know).

The difference with the mass is that in the case of the mass, the Standard Model (SM) does not allow a mass term per se. It is only once the Higgs field takes a non-zero vacuum expectation value (vev) that breaks the SM gauge symmetry that particles obtain an effective mass from the Higgs vev and their interactions with it.

 

[Berbit]

The charge of a particle by definition is its fundamental interaction strength with the photon field. This is a property of the particle itself and not the result of any other field (as far as we know).

The difference with the mass is that in the case of the mass, the Standard Model (SM) does not allow a mass term per se. It is only once the Higgs field takes a non-zero vacuum expectation value (vev) that breaks the SM gauge symmetry that particles obtain an effective mass from the Higgs vev and their interactions with it.

Thank you, that helps. Perhaps you can clarify this comment, which I read in a Sean Carroll book: 'If not for the Higg's Field, the electron and electron neutrino would be the same particle' (and I suppose all leptons would be the same particle). Following this, how does interacting with the Higg's give the electron charge? Seems somehow not fundamental here.

Separately, you commented "(SM) does not allow a mass term per se." I don't quite know what this means (beyond a general sense)-- how is this formulated? Truthfully, not sure that this is a question that can be answered here!

 

[Berbit]

The charge of a particle by definition is its fundamental interaction strength with the photon field. This is a property of the particle itself and not the result of any other field (as far as we know).

The difference with the mass is that in the case of the mass, the Standard Model (SM) does not allow a mass term per se. It is only once the Higgs field takes a non-zero vacuum expectation value (vev) that breaks the SM gauge symmetry that particles obtain an effective mass from the Higgs vev and their interactions with it.

Hello Again,
Separate question for same post-- you mention the charge being based on the fundamental interaction strength with the photon field. So are these interaction strengths then quantized in units (multiples) of e (or 1/3e)?

 

[Fervent Freyja]

"(SM) does not allow a mass term per se." I don't quite know what this means (beyond a general sense)-- how is this formulated? Truthfully, not sure that this is a question that can be answered here!

"Per se" is a huge understatement. Generally, the SM implies no mass at all, it is formulated with symmetry that cancels out any mass. Hence, the Higgs mechanism is required.

 

[Berbit]

"Per se" is a huge understatement. Generally, the SM implies no mass at all, it is formulated with symmetry that cancels out any mass. Hence, the Higgs mechanism is required.

Hello FF,
Thank you, yes, I understand that aspect of the Higgs (at least superficially). I've read Sean Carrol state that without the Higgs the leptons would be the same particle, including, for example, the electron and the e-neutrino. This sounds like the Higgs is then responsible for charge as well. Am I missing something? Perhaps the comment is in context of the strong force only?

 

[Fervent Freyja]

I missing something? Perhaps the comment is in context of the strong force only?

You are welcome. To be honest, you won't miss as much if you choose to only read textbooks or use your time wisely on the more credible resources out there. I cut out the popular science books/magazines/websites pretty quickly, they send you in circles.

 

[Berbit]

You are welcome. To be honest, you won't miss as much if you choose to only read textbooks or use your time wisely on the more credible resources out there. I cut out the popular science books/magazines/websites pretty quickly, they send you in circles.

Wise words! So I must bother you once more: got a recommendation?

 

[Drakkith]

Ive read Sean Carrol state that without the Higgs the leptons would be the same particle, including, for example, the electron and the e-neutrino. This sounds like the Higgs is then responsible for charge as well. Am I missing something? Perhaps the comment is in context of the strong force only?

I wouldn't try to infer much about physics from statements like this. It's likely that Carrol's comment has little to no bearing on the origin of charge. If you find a source that lays out a theoretical and mathematical basis for this, or at least explicitly says, "The higgs mechanism is responsible for the origin of charge", that's when you should take it seriously.

 

[mfb]

"Per se" is a huge understatement. Generally, the SM implies no mass at all, it is formulated with symmetry that cancels out any mass. Hence, the Higgs mechanism is required.

The Higgs mechanism is part of the SM. The SM has masses for all particles apart from neutrinos, photons and gluons.

 

[Orodruin]

I wouldn't try to infer much about physics from statements like this. It's likely that Carrol's comment has little to no bearing on the origin of charge. If you find a source that lays out a theoretical and mathematical basis for this, or at least explicitly says, "The higgs mechanism is responsible for the origin of charge", that's when you should take it seriously.

In some sense, the Higgs mechanism decides what "electric charge" is by selecting a direction for the Higgs vev. What is the remaining U(1) symmetry is exactly the gauge transformation that preserves the Higgs vev. I would not say that this means that the Higgs is "responsible for charge". The symmetry was there before symmetry breaking as well.

Whether or not one calls the electron and electron neutrino "the same particle" before symmetry breaking is a matter of bookkeeping and taste. There was a thread a while back where the counting of particles was discussed. Also, the electron neutrino would be indistinguishable from the left-handed electron as the are just the different components of an SU(2) doublet. However, the right-handed neutrino would be distinct as it is an SU(2) singlet.

 

[ChrisVer]

However, the right-handed neutrino would be distinct as it is an SU(2) singlet.

if there is...

 

[Orodruin]

if there is...

Oooops. I must have an occupational injury that distorted my thought on the way from my head to the keyboard. I meant to say right-handed electron.

Of course, the right-handed neutrino would be a singlet under all SM gauge groups if it exists.

 

[nikkkom]

Hello FF,
Thank you, yes, I understand that aspect of the Higgs (at least superficially). I've read Sean Carrol state that without the Higgs the leptons would be the same particle, including, for example, the electron and the e-neutrino.

This is subtly wrong. "Electron and the e-neutrino would be the same particle" only in a sense that green quark and blue quark are often said to be "one type of particle", just quark. But in many cases, they have to be counted as separate types of particles.

If you remove Higgs field from SM, the electroweak force will not reduce to electromagnetism, it will be still "unbroken" and consist of:

Weak hypercharge force, with properties very similar to electromagnetism - massless uncharged B bosons quanta are carriers, each left-handed lepton has -1 weak hypercharge, each right-handed electron-type lepton has -2 weak hypercharge. (Right-handed neutrinos, if they exist, have 0 charge).

Weak isospin force, an always attractive force with three carriers W1, W2 and W3 who are themselves charged under weak isospin. It's somewhat similar to gluons and quarks, but having 2 "colors" instead of 3: they are called "up" and "down". Electrons and neutrinos are different here: left-handed electrons are "down"-particles, left-handed neutrinos are "up"-particles. W1 and W2 turn them into each other, W3 rotates the phase of their two components in opposite directions but doesn't mix components (which means it does not change "up"/"down"-ness). Right-handed particles are not charged under weak isospin. Unlike gluons and quarks, weak isospin force is not strong enough to exhibit containment: it does weaken with distance.

This picture is "spoiled" by the fact that not only Higgs, but QCD also has a quark-antiquark vacuum condensate (nonzero VEV), so there would be a much weaker form of higgs-like mechanism which would give (smaller) masses to particles.

 

[Vanadium 50]

In some sense, the Higgs mechanism decides what "electric charge" is by selecting a direction for the Higgs vev. What is the remaining U(1) symmetry is exactly the gauge transformation that preserves the Higgs vev. I would not say that this means that the Higgs is "responsible for charge". The symmetry was there before symmetry breaking as well.

I agree. More importantly, if the vev were to point in a different direction, we would still have electric charge. An interesting exercise is to try and figure out which constants would change and what, if any, changes there would be to the universe, but the basic theory of electromagnetism is still there, because you still have an unbroken U(1) after SU(2) x U(1) breaks.

 

[nikkkom]

I agree. More importantly, if the vev were to point in a different direction

What does this mean? I thought the "direction" of Higgs VEV can be rotated arbitrarily via gauge choice and thus is unphysical?

 

[Orodruin]

What does this mean? I thought the "direction" of Higgs VEV can be rotated arbitrarily via gauge choice and thus is unphysical?

Yes, it is just a matter of what basis you pick for the fundamental representation of SU(2). Introducing a vev for a scalar in the fundamental representation will always leave one unbroken direction. This direction corresponds to electromagnetism.

 

[ohwilleke]

Hello FF,
Thank you, yes, I understand that aspect of the Higgs (at least superficially). I've read Sean Carrol state that without the Higgs the leptons would be the same particle, including, for example, the electron and the e-neutrino. This sounds like the Higgs is then responsible for charge as well. Am I missing something? Perhaps the comment is in context of the strong force only?

I think that you are reading more into Sean Carroll's simplification of the physics than it can bear. The Higgs field is absolutely not responsible for electromagnetic charge.

I suspect that what he means to say is that absent the Higgs field, electrons and electron neutrinos would both be massless, would both be first generation leptons bearing lepton number, would both lack color charge, and the electron neutrino would not oscillate as a real massive electron neutrino does because only massive neutrinos can oscillate. Their weak force interactions would be identical except that the neutrino is only left handed (or right handed if an antiparticle). The only differences between them would be electric charge and as a result of lack of electric charge in the neutrino, and a reduction in available CP combinations from 4 to 2.

Also, in the absence of the Higgs field it isn't clear how generations of leptons would be distinguishable, as electrons-muons-taus and their counterpart neutrinos are each identical except for mass and for decays that are fully derived from mass and not a fundamental property of the particles. The Higgs is a necessary component of a three generations of fermion structure in the SM that makes any sense.