Creation of singlets: charge conservation?

[nomadreid]

When massless particles are given mass by the Higgs mechanism, then there is no problem with charge conservation if a matter-antimatter pair is created. But what happens when a single charged particle is created? Where happens to the conservation of charge?

 

[Bill_K]

Not sure what you're asking. Maybe you're asking this: "Massless particles have two states and massive particles have three. So where do the third charged states for the W+ and W- come from?"

The answer is, you actually add four scalar fields into the Lagrangian, arranged as an isospin doublet of complex fields. Two of these fields are charged while two of them are neutral. The Higgs mechanism turns three of them into additional states for W+, W- and Z, leaving one neutral field, which becomes the Higgs field.

(If that's not what you're asking, ask again.)

 

[nomadreid]

Thanks for the answer, Bill_K, and your readiness to try again if needed. It is needed, because my question was a bit different, simpler, on a more elementary level, and possibly a bit simple-minded, as I am not a physicist. Rather, I am trying to get my way through the popular literature on the Higgs mechanism. So, I shall try to be more explicit.

From what I understand, massless particles do not have charge, hence in the interaction with the Higgs field, not only do they acquire mass, but some of them acquire charge. I am not sure of how the charge acquisition is accomplished, but even skipping over that for the moment, there seem to be two cases: the more common one when a pair of matter-antimatter particles is created, and two, when only a single particle is created. (Actually, perhaps I should have started with the question whether it is correct that this second case does actually occur. I know that the popular literature is not always to be trusted.) In the case of the matter-antimatter pair production, since the charge of the massless particle was zero, and the sum total of the matter and antimatter particles will also necessarily be zero, so electric charge is conserved. However, if there is only a single particle created, can it have charge? Or is it never the case that a single particle is created? If a single charged particle can be created, then it would seem that charge is not conserved. In this case, would that mean that charge conservation is not an absolute?

While I am on the subject, I have also read that some particles, such as certain neutrinos and certain B-mesons, spontaneously oscillate between one state and another, from the particle to their respective antiparticles. Do any of the particles that do this have an electric charge? If so, would this be a violation, albeit temporary, of the conservation of charge?

I hope the questions do not appear too naive, even for a non-physicist such as myself.

 

[negru]

Charge is always conserved, and both neutrinos and B-mesons are neutral. There's no uncertainty principle for charge, if that's what you're thinking.

 

[nomadreid]

both neutrinos and B-mesons are neutral.

Ah, that clears up a lot. Of course (silly me ) neutrinos are neutral, but I see that there are positively charged B-mesons (with negatively charged antiparticles). But I presume you mean that the ones which do the switching are neutral. So, if a singlet is created, it is going to be neutral. One last question, just to make sure: are singlets created in the Higgs mechanism, or are they always produced in pairs?
Many thanks.

 

[negru]

Well you don't have to associate pair production with the Higgs. You could have pair production without any higgs - you'd just have massless particles. the higgs just gives mass to the what would have otherwise been massless particles. The Higgs mechanism doesn't create anything.

And particle creation always comes in pairs, the two need to annihilate each other. otherwise the unc. princ. would be violated. (and possibly other principles depending on the particle)

 

[nomadreid]

Well you don't have to associate pair production with the Higgs. You could have pair production without any higgs - you'd just have massless particles. the higgs just gives mass to the what would have otherwise been massless particles. The Higgs mechanism doesn't create anything.

Ah, I had not considered that. Thanks.

And particle creation always comes in pairs, the two need to annihilate each other. otherwise the unc. princ. would be violated. (and possibly other principles depending on the particle)

This would seem to be a definite negative to my question: that is, singlets are never created. Thanks, negru.
But this leads me to three related questions.
(1) In (certainly over-simplified) explanations about the annihilation of an electron and a positron, it is stated that the opposite charges attract each other, so that they come together. If this were the only mechanism, then a neutron and an anti-neutron would not necessarily re-unite to annihilate, but you are saying that they must. So, what forces the particle and anti-particle together, outside of the need to obey the uncertainty principle?
(2) In the pair production, no new energy is created or destroyed, so would the non-annihilation of the two particles somehow determine simultaneously position and momentum, or Energy and time period, or what? (I am sure this is an elementary question, so I will be the more grateful for the answer.)
(3) Related to (2): A particle and an anti-particle do not always annihilate each other, as in the cases of Hawking radiation and of the Uhruh effect, if I understand these hypothetical phenomena more or less correctly. So, does the hiding of the information of one of the particles then save it from violating the Uncertainty Principle?

Thanks again.

P.S. It occurs to me that if no singlets are ever created, then the giving of mass to massless particles only occurs after pair production. Why is that, if the Higgs mechanism is independent of the production of pairs? There are massless particles that are not pairs, so why are not they affected by the Higgs mechanism?

 

[BHamilton]

(1) In (certainly over-simplified) explanations about the annihilation of an electron and a positron, it is stated that the opposite charges attract each other, so that they come together. If this were the only mechanism, then a neutron and an anti-neutron would not necessarily re-unite to annihilate, but you are saying that they must. So, what forces the particle and anti-particle together, outside of the need to obey the uncertainty principle?

Nothing. If I have an antineutron here, and neutron there, they just kinda sit there and do their thing until you bring them together by some other means. It's just that a system of an electron and positron has its own mechanism to bring the two together.

(2) In the pair production, no new energy is created or destroyed, so would the non-annihilation of the two particles somehow determine simultaneously position and momentum, or Energy and time period, or what? (I am sure this is an elementary question, so I will be the more grateful for the answer.)

I'm not sure what you're asking here. If pair creation takes place in a vacuum, then the pairs are "virtual" in that they don't obey the relationship E^2 - p^2 = m^2. The jargon is that they are "off mass shell". Now, to propagate through spacetime normally, a particle cannot be "off mass shell", it must be on it's mass shell. What this boils down to is that if you want the pair to stick around as actual honest to goodness "real" particles, you have to add energy/momentum to them somehow. In pair creation from a gamma ray, for instance, it's interactions between the produced electron/positron and the material the gamma ray is traveling through that allows the process to proceed.

(3) Related to (2): A particle and an anti-particle do not always annihilate each other, as in the cases of Hawking radiation and of the Uhruh effect, if I understand these hypothetical phenomena more or less correctly. So, does the hiding of the information of one of the particles then save it from violating the Uncertainty Principle?

In the case of hawking radiation, gravitational interaction with the black hole gives the energy/momentum to the system needed for the particles to be "real".

P.S. It occurs to me that if no singlets are ever created, then the giving of mass to massless particles only occurs after pair production. Why is that, if the Higgs mechanism is independent of the production of pairs? There are massless particles that are not pairs, so why are not they affected by the Higgs mechanism?

Again I'm not sure where you're going with this. The higgs field is in such a state that all of space is filled with a constant higgs field. The picture at the level of particles is that as the particle moves through space, it continually interacts with the nonzero higgs field (in some sense constantly scattering off of it). If you do the math, the net effect of this interaction on a massless particle is to make it behave as if it were a massive particle.

 

[nomadreid]

BHamilton: thank you very much for your answer; it cleared up several points. There is still a question left over which, I admit, was not properly expressed (so you said that you weren't sure where I was going with my question), so I will try to be clearer, hoping that your patience stretches this far. (I no longer need to drag Higgs into the remaining question, though.)

First, a preliminary question : a virtual antineutron and a virtual neutron produced in pair production will of course annihilate, since they would otherwise violate the uncertainty principle, unless, as you mentioned, something gives them the necessary energy/momentum to become real. However, it would seem that pair production where energy is transformed into two particles with the same total energy equivalent, modulo their net momentum, as the opposite process to the annihilation of a real neutron and a real antineutron, would be a possible evolution of a photon with sufficient energy. Is this incorrect? If it is a possibility, then when that does happen, since neither electromagnetic attraction nor necessity to blink out in order to not offend the uncertainty principle require them to disappear, it would be thinkable that they would stick around. No? If not, why not?

Now, if real particles can be produced, either by the possibility above or by virtual particles turning real, is it possible for an electrically neutral single real particle to be produced instead of a pair? If not, why not?

Thanks.

 

[BHamilton]

However, it would seem that pair production where energy is transformed into two particles with the same total energy equivalent, modulo their net momentum, as the opposite process to the annihilation of a real neutron and a real antineutron, would be a possible evolution of a photon with sufficient energy. Is this incorrect? If it is a possibility, then when that does happen, since neither electromagnetic attraction nor necessity to blink out in order to not offend the uncertainty principle require them to disappear, it would be thinkable that they would stick around. No? If not, why not?

They aren't quite reversed processes. When a particle/antiparticle pair annihilate, photons always come out in pairs or threes because otherwise energy and momentum can't be conserved (a simple way to see it in this case is that the pair has some well-defined rest frame, whereas a single photon cannot possibly have a well-defined rest frame).

But cutting straight to the point, we know of no particles that can be singly produced from the vacuum. From the point of view of theory, there simply isn't a way to get a single particle out of vacuum fluctuations. If you try to insert the kinds of interactions you would need to make this happen, then you can show that the vacuum that results is a false vacuum, and the true vacuum is such that this process doesn't happen.

 

[nomadreid]

Thanks, BHamilton. That was a big help.

 

[Bill_K]

The Higgs mechanism doesn't create anything.

It creates a third state for vector bosons. Massless bosons have two polarization states, while massive ones have three.