Is Weak Hypercharge Conserved in Particle Interactions?

[Phrak]

Charge is conserved in particle interactions. Color is conserved. Inerial mass is conserved locally. Is weak hypercharge conserved?

 

[malawi_glenn]

http://en.wikipedia.org/wiki/Weak_hypercharge

 

[Sideways]

Yes it is.

The wikipedia article is pretty good if you want to learn more.

(By the way, Jefferson Laboratory in Newport News, Virginia is soon starting a major experiment to measure the weak charge of the proton.)

According to electroweak unification theory (part of the Standard Model), weak hypercharge ties directly into the electromagnetic properties of particles.

 

[humanino]

By the way, Jefferson Laboratory in Newport News, Virginia is soon starting a major experiment to measure the weak charge of the proton.

I thought Jefferson Lab was a place were people study the strong interaction. Why did they decide to measure the weak charge ? Because they can ? Can they ? How difficult will this be ?

 

[Sideways]

I thought Jefferson Lab was a place were people study the strong interaction. Why did they decide to measure the weak charge ? Because they can ? Can they ? How difficult will this be ?

JLab was originally made strictly as an electromagnetic probe of nucleons and nuclei, but their mission has expanded a bit. It's a very tricky experiment; it will take something like a year of running time in one of the 3 research halls, if I recall correctly.

Layman's description of the experiment:

http://www.jlab.org/qweak/

 

[humanino]

It's a very tricky experiment; it will take something like a year of running time in one of the 3 research halls, if I recall correctly.

Your statement is very misleading. It will take the entire tentatively scheduled beam time of JLab's Hall C for 3 years. Some people must have considered they had to deeply update JLab's mission. I'm not sure to get the point when I see the projected plot

 

[Phrak]

Yes it is.

The wikipedia article is pretty good if you want to learn more.

(By the way, Jefferson Laboratory in Newport News, Virginia is soon starting a major experiment to measure the weak charge of the proton.)

According to electroweak unification theory (part of the Standard Model), weak hypercharge ties directly into the electromagnetic properties of particles.

I didn't see anything in the Wikipedia article motivating weak charge conserveration. A little more searching, and I didn't find anything motivation conservation of electric charge within quantum field theory, either. I don't see the symmetry that would motivate either charge.

Why should electric, the weak charge, or their composite be conserved?

 

[malawi_glenn]

electric charge is conserved if you do the Noethers theorem. Same with weak charge.

 

[Vanadium 50]

I'm afraid I am going to have to disagree with the majority (and Wikipedia). I don't see how weak hypercharge can possibly be conserved. The left-handed and right-handed electrons have different weak hypercharge. I can flip the spin with a magnetic interaction: $e_L + \gamma \rightarrow e_R + \gamma$, and now the left and right hand sides of the equation have different weak hypercharge.

Furthermore, if it were conserved, it's gauge field, the B, would be massless. It's not - it's not even in an eigenstate of mass.

Weak hypercharge is a broken symmetry. If the symmetry were unbroken, it would be conserved. But that's not the universe we live in.

 

[Phrak]

electric charge is conserved if you do the Noethers theorem. Same with weak charge.

Which symmetry and variation of Noether's theorem applies?

 

[malawi_glenn]

Pick up any source on intro QED

 

[Phrak]

Pick up any source on intro QED

Malawi! you're so inegmatic. Can I buy a clue? Where in Weinberg?

 

[malawi_glenn]

Well if you can agree that Maxwells equations state conservation of electrc charge then QED should have that property. I don't have my Weinberg at home, but if you have peskin the argument is in ch3 "quantization of the Dirac field", see page 62.

 

[Phrak]

Well if you can agree that Maxwells equations state conservation of electrc charge then QED should have that property. I don't have my Weinberg at home, but if you have peskin the argument is in ch3 "quantization of the Dirac field", see page 62.

Thanks for responing so quickly. Weinberg vol. I is all I have.

But that's interesting. I get charge convervation in Maxwell via other means than Noether. It results from the Maxwell tensor being antisymmetric. [tex]F_{\mu\nu}=F_{[\mu\nu]}

I can't identify the argument in Weinberg, volume I.

 

[malawi_glenn]

oh let me see if I can help you with that, since you have that the Maxwell tensor (aka electromagnetic field tensor) is antisymmetric, we have $$\partial _\nu F^{\mu \nu} = 0$$ so that we get the equation of continuity for electric charge. But another way to see this is by considering the action $$S = \int F^{\mu \nu}F_{\mu \nu} d^4x$$ and using noethers theorem on that one and euler lagrange equation of motion.

Weinberg is perhaps not the best place to start QFT... Mandl or Peskin is probably better introductory books.

Now I am not an expert on the electroweak theory (yet) but I have to say now that Vanadium seems to be entirely correct and that wiki article should be edited/motivated

 

[Phrak]

oh let me see if I can help you with that, since you have that the Maxwell tensor (aka electromagnetic field tensor) is antisymmetric, we have $$\partial _\nu F^{\mu \nu} = 0$$ so that we get the equation of continuity for electric charge. But another way to see this is by considering the action $$S = \int F^{\mu \nu}F_{\mu \nu} d^4x$$ and using noethers theorem on that one and euler lagrange equation of motion.

Weinberg is perhaps not the best place to start QFT... Mandl or Peskin is probably better introductory books.

Now I am not an expert on the electroweak theory (yet) but I have to say now that Vanadium seems to be entirely correct and that wiki article should be edited/motivated

Wonderful! That's what I needed to get started, I'm sure. You know, this is all Vanadium's fault in the first place. He's the one who got me started on this.

 

[malawi_glenn]

hahahaha yeah blaim him ;-) He is a real trouble maker :-D

 

[Phrak]

malawi, thanks for all your help. I hope you keep this thread subscribed.

This is a very interesting issue for me. One the one hand, electric charge conservation is a direct result of simply imposing a 4-vector field on a (pseudo) Riemann manifold, of any Christoffel connection, and the definition of charge as the divergence of E--nothing more.

I don't know how far you've gone in the mathematical angle of differentiable manifolds, but charge conservation is summed-up in the statement, "All exact forms are closed."

On the other hand, the usual method of finding conservation laws is via Noether, as you know.

Are these two derivations the same or different?
It could be shocking and profound if they cannot be found equivalent.

I have to learn Noether.

 

[malawi_glenn]

malawi, thanks for all your help. I hope you keep this thread subscribed.

This is a very interesting issue for me. One the one hand, electric charge conservation is a direct result of simply imposing a 4-vector field on a (pseudo) Riemann manifold, of any Christoffel connection, and the definition of charge as the divergence of E--nothing more.

I don't know how far you've gone in the mathematical angle of differentiable manifolds, but charge conservation is summed-up in the statement, "All exact forms are closed."

On the other hand, the usual method of finding conservation laws is via Noether, as you know.

Are these two derivations the same or different?
It could be shocking and profound if they cannot be found equivalent.

I have to learn Noether.

No Noether is as far as I know something different, but iam not 100% sure.

I've only done differntial geometry in class of General Relativity and one class in advanced analytical mechanics.

 

[Phrak]

No Noether is as far as I know something different, but iam not 100% sure.

I've only done differntial geometry in class of General Relativity and one class in advanced analytical mechanics.

It's hard to say for me at this early date. Either way it should be interesting.

With some preliminary reading of Noether, this will take some time. I see that the Lagrangian $$\ F_{\mu\nu}F^{\mu\nu}$$ doesn't allow for field divergence. There are other formulations that include it. It's doesn't appear to be covariant--if not, it's applicable to Minkowski space, but not to Riemann Manifolds in general--but Minkowski space is the space used in particle physics, anyway. There are all sorts of issues, I need to resolve (and some review, as well!). I'd like to eventually see how it generalized to the electroweak force.

You could drop this thread and I'll pick it up later, I hope. But if you're interested in electromagnetism where the antisymmetry of the electromagnetic field tensor implies charge conservation, you could read Sean Carroll's Lecture Notes on General Relativity, available online in pdf format. His notes won't tell you about the antisymmetry of F_{\mu\nu} implying charge conservation; but it will introduce you to the powerful notation of differential forms that does.

 

[malawi_glenn]

The thing is that Noeather is for field theories, and you'll have noether in QFT's aswell.

Yes, I have seans notes, and I know from Rindlers books in SR how Fmu nu antisymmetri implies charge consv.

Just bump this thread if you want to discuss more later =)

 

[Phrak]

The thing is that Noeather is for field theories, and you'll have noether in QFT's aswell.

Yes, I have seans notes, and I know from Rindlers books in SR how Fmu nu antisymmetri implies charge consv.

Good grief. Is there anything I know that someone else doesn't already know better? It's even in a book.

Just bump this thread if you want to discuss more later =)[/QUOTE]

Thanks much!

 

[hagi]

I can flip the spin with a magnetic interaction: $e_L + \gamma \rightarrow e_R + \gamma$, and now the left and right hand sides of the equation have different weak hypercharge.

If I'm right, your point is that an external field interaction can alter the chirality of a particle. On the other hand, you say that the spin gets flipped. But since an electron is massive, it can be in both helicity states so if its spin flips, its helicity gets changed but the chirality does not.

I was tought in my QFT class that in the non-relativistic case, the spin is conserved while in the relativistic limit the helicity is conserved which would even say that it's not possible to flip the spin of a particle whose mass we can ignore. In this case the helicity is the same thing as the chirality, which is conserved so in the relativistic limit the helicity must also be conserved!

 

[Neutrino1]

Hi folks,

You have to be super-careful here about whether you are talking about symmetries of the Lagrangian (which generate conserved quantities) or the theory after spontaneous symmetry breaking and the mixture of weak hypercharge and one component of the weak isospin. I found the following reference to be useful:

http://books.google.com/books?id=we...a=X&oi=book_result&ct=result&resnum=7#PPP1,M1

Look at around page 100 for a very clear discussion.

Hope that is a help.

 

[Bob Zannelli]

Vanadium is correct. Weak charge is not strictly conserved as are electric or color charge for example, though you find many physicists arguing it is. Gauge symmetries actually exist in the context of zero mass force carrying particles, in the weak sector this symmetry is broken by the Higgs field. ( We think) BTW the same may hold for B-L charge which is gauged in left right symmetry models. ( Pati Salam)

 

[Ben Niehoff]

As for the discussion about electric charge: Electric charge is the Noether charge associated with global gauge symmetry.

You can derive charge conservation from Maxwell's equations also, of course. But to do it using Noether's theorem, you have to vary the Lagrangian by a global gauge transformation.