Is the electric charge of bosons w1 w2 w3 well defined?

[arivero]

It seems that we are mixing -ahem- two different questions.

a) about the pure theory, with SU(2)xU(1) and not fermion content at all. Then the question is if there is a sensible choosing for an U(1) "electromagnetic" subgroup or if any subgroup will give W^+ a charge of one unit.

b) about the theory with electrons and neutrinos. Then we can require the coupling of the U(1) to be equal for left and right electrons (and its value actually defines the electric charge) and zero for neutrinos, and the the point is how arbitrary the hypercharge assignments for the neutrino and left and right electron can still be.

Both questions are, it seems to me, well formulated before symmetry breaking. Just for peace of mind, you can change the sign in the quadratic term of the higgs field and voila, you are in the unbroken theory.

The mixing a+b allows for a third question (perhaps it can be already done just in (a), can it?): if the charge that W^+ "carries" is also the same charge that it presents when we compute the WW\gamma vertex.

 

[naima]

I'd like to come back to my initial problem.
In local gauge theories we add fields to the derivative so as to get it covariant.(eg w1 w3 w3)
Actually the exchanged bosons are W+ W- and W3. (W+ = W1 - iW2 and so on)
What is the trick to get these "physical" bosons out of first ones in general ? (eg in SU(5), SO(10) ..)

 

[arivero]

I'd like to come back to my initial problem.
In local gauge theories we add fields to the derivative so as to get it covariant.(eg w1 w3 w3)
Actually the exchanged bosons are W+ W- and W3. (W+ = W1 - iW2 and so on)
What is the trick to get these "physical" bosons out of first ones in general ? (eg in SU(5), SO(10) ..)

Well, I thought that your initial problem was really my question (a) above, or the a+b, perhaps.

As for what are these bosons you call "physical", it is more of a question on group (or lie algebra) representation theory, isn't it? It seems that "ladder operators", who are used to produce the whole representation, are the important ones. SU(2) as a single ladder operator, W+.

 

[kurros]

b) about the theory with electrons and neutrinos. Then we can require the coupling of the U(1) to be equal for left and right electrons (and its value actually defines the electric charge) and zero for neutrinos, and the the point is how arbitrary the hypercharge assignments for the neutrino and left and right electron can still be.

I agree with you, but is there a reason we should care if the left and right electrons have equal coupling if there is no symmetry breaking? Since they are massless they propagate entirely separately from each other and they are in different group representations, so is not our effort to associate them with each other arbitrary?

 

[DrDu]

I'd like to come back to my initial problem.
In local gauge theories we add fields to the derivative so as to get it covariant.(eg w1 w3 w3)
Actually the exchanged bosons are W+ W- and W3. (W+ = W1 - iW2 and so on)
What is the trick to get these "physical" bosons out of first ones in general ? (eg in SU(5), SO(10) ..)

As long as your symmetry isn't broken, you could use instead of f and f' as basis states the combinations 1/√2 (f+f') and 1/√2 (f-f') or 1/√2(f+if') and 1/√2(f-if'), which would be interchanged by something like w2±iw3 and w1±iw3, respectively. So before symmetry breaking, there is no reason to single out a special combination of the w_i.

 

[arivero]

I agree with you, but is there a reason we should care if the left and right electrons have equal coupling if there is no symmetry breaking? Since they are massless they propagate entirely separately from each other and they are in different group representations, so is not our effort to associate them with each other arbitrary?

I can not think of a reason internal to the model. Perhaps quantization anomalies could have a role? Externally some arguments could ask for Dirac-like instead of Weyl particles. For instance, to be able to formulate electromagnetism in a Kaluza Klein way, or to need to fit in a given way inside a GUT group. Or empirical input itself.

 

[arivero]

As long as your symmetry isn't broken, you could use instead of f and f' as basis states the combinations 1/√2 (f+f') and 1/√2 (f-f') or 1/√2(f+if') and 1/√2(f-if'), which would be interchanged by something like w2±iw3 and w1±iw3, respectively. So before symmetry breaking, there is no reason to single out a special combination of the w_i.

Ah, OK, I had missed this, of course you can choose any U(1)_L inside SU(2)_L to fix W3, I though the main discussion was about choosing U(1) from U(1)_L x U(1)_Y. The only reason is that someone can, and then must, mix with U(1)_Y, so whatever you choose, that one is W3, irrespective or breaking or not.

 

[naima]

If you think observables like momenta, charges (and their operators) are fundamental,
there is a difference between eigenstates and non eigenstates.
for the electic charge w1 is not like w1 -iw2

 

[DrDu]

If you think observables like momenta, charges (and their operators) are fundamental,
there is a difference between eigenstates and non eigenstates.
for the electic charge w1 is not like w1 -iw2

Ok, but as long as symmetry isn't broken, you can choose equally tau_1, tau_2 or tau_3 as charge and the three don't commute with each other. Symmetry breaking sigles out one element of the algebra which we then choose to call tau_3.

 

[arivero]

The cleaning lady found a copy of Weinberg's "A Model of Leptons" (PhysRev 1967) in the WC and let it on the clothes bag, I noticed it today. Point is, that it seems that in the sixties they was no doubt about the normalisation of the hypercharge: you link it to the lepton number, via N=N_R+N_L and Y=N_R+1/2 N_L. It was only a puzzle that the lepton number is not a local gauge quantity.

 

[naima]

I received this from prof Elbaz

"Thank you for your mail and your interest in one of my books. I quite agree with you because the mixing angles merely reflect the weight of the mixture of electrically charged leptons. If the symmetry breaking must bring the mass to the particles, it can do that only on already existing particles"

I recall you this lines found on WIKI

"he electroweak epoch began when the strong force separated from the electroweak interaction. Some cosmologists place this event at the start of the inflationary epoch, approximately 10-36 seconds after the Big Bang.[1][2][3] Others place it at approximately 10-32 seconds after the Big Bang when the potential energy of the inflation field that had driven the inflation of the universe during the inflationary epoch was released, filling the universe with a dense, hot quark-gluon plasma.[4] Particle interactions in this phase were energetic enough to create large numbers of exotic particles, including W and Z bosons and Higgs bosons. As the universe expanded and cooled, interactions became less energetic and when the universe was about 10-12 seconds old, W and Z bosons ceased to be created. The remaining W and Z bosons decayed quickly, and the weak interaction became a short-range force in the following quark epoch.""

If as you told it repeatedly this is wrong be courageous MODIFY the http://en.wikipedia.org/wiki/Electroweak_epoch" or at less
write that you disagree in its Talk section.

 

[kurros]

I received this from prof Elbaz
"Thank you for your mail and your interest in one of my books. I quite agree with you because the mixing angles merely reflect the weight of the mixture of electrically charged leptons. If the symmetry breaking must bring the mass to the particles, it can do that only on already existing particles"

Perhaps you could post the question you asked him. His answer doesn't tell me much on it's own.

I recall you this lines found on WIKI

"he electroweak epoch began when the strong force separated from the electroweak interaction. Some cosmologists place this event at the start of the inflationary epoch, approximately 10-36 seconds after the Big Bang.[1][2][3] Others place it at approximately 10-32 seconds after the Big Bang when the potential energy of the inflation field that had driven the inflation of the universe during the inflationary epoch was released, filling the universe with a dense, hot quark-gluon plasma.[4] Particle interactions in this phase were energetic enough to create large numbers of exotic particles, including W and Z bosons and Higgs bosons. As the universe expanded and cooled, interactions became less energetic and when the universe was about 10-12 seconds old, W and Z bosons ceased to be created. The remaining W and Z bosons decayed quickly, and the weak interaction became a short-range force in the following quark epoch.""

If as you told it repeatedly this is wrong be courageous MODIFY the http://en.wikipedia.org/wiki/Electroweak_epoch" or at less
write that you disagree in its Talk section.

When did anyone say this was wrong? Of course it became a short range force once the gauge bosons became massive.

 

[naima]

Hi Kurros
This a part of the text of my email:

I try to show in a forum, as you did (and as Zuber), that the introduction of electrically charged leptons, currents carried by the charged W-W+, mixing angles, PRECEDE symmetry breaking. It is visibly against ambient ideas. Watch as the article "electroweak interaction" on wikipedia. Which argument could move forward on this issue?

recall several previous posts:

No - you have given the fermions electric charge. Before symmetry breaking, you don't have electric charge. .

Before symmetry breaking you don't have a photon. .

The wiki page you link to alludes to this without explaining it terribly much:

"In the Standard Model, the W± and Z0 bosons, and the photon, are produced by the spontaneous symmetry breaking of the electroweak symmetry from SU(2) × U(1)Y to U(1)em, caused by the Higgs mechanism (see also Higgs boson).[3][4][5][6] U(1)Y and U(1)em are different copies of U(1); the generator of U(1)em is given by Q = Y/2 + I3, where Y is the generator of U(1)Y (called the weak hypercharge), and I3 is one of the SU(2) generators (a component of weak isospin)."

I.e. you do not have Q (electric charge) until you have U(1)em, which is only a useful thing to talk about after symmetry breaking happens. Your leptons do however have Y (hypercharge), which tells you things about how they interact with the B gauge bosons, and is basically an exact copy of how electric charge works, but it is in fact different.

if electric charged left electrons and left neutrinos were (before break) eigenvectors
don't you think that they defined a preferred T3 direction in the isospin space?

another question: are the g g' coupling running constant before breaking and did the mixing angle
remained constant before and after the break?

 

[kurros]

Are you arguing against the choice of words that no electric charge or photon exists before symmetry breaking? Because I think it has been said here that yes, before symmetry breaking there exist charges and gauge bosons of which the electric charge and photon are a mixed subset.

As for whether the existence of the leptons already defines as direction in isospin space, I don't know, but I was under the impression that they did not. After all the unbroken electroweak Lagrangian is symmetric under SU(2) transformations by construction, so whatever isospin direction we pick out could be immediately rotated into some other isospin direction and nothing would change, surely.

As for the gauge coupling running, they run all the time, it has nothing to do with symmetry breaking. The weak mixing angle runs likewise, although again I don't think it makes much physical sense above the symmetry breaking scale. You can probably still define it and use it though. Actually maybe not, it can be defined in terms of the masses of the W and Z bosons, which vanish above the weak scale, so it might be undefined there.