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jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Sat Oct 21, 2006 2:44 pm Post subject: Parity Violation at E158 


Martin.Grunewald@cern.ch
Fri 20041001 8:51 AM
Dear Professor Grunewald,
Recently, I have noticed that you have cited E158 paper “Observation of Parity Nonconservation in Moller Scattering” in your preprint.
However, there is one thing I could not figure out in E158 paper. As long as I know, the helicity of a massive particle is not definite, since we can always find a boosted frame of reference in which the helicity is the opposite. Therefore, E158 measurment of helicity of electron or muons is only that of laboratory frame and it implies Lorentz violation.
I would like to appreciate if you can explain this issue.
I sincerely apologize for your time and effort if you find it unworthy of your attention.
I am looking forward to hearing from you.
Thanks,
J.C. Yoon 

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Martin Gruenewald
Joined: 28 Sep 2006 Posts: 5

Posted: Sat Oct 21, 2006 2:46 pm Post subject: Re: Parity Violation at E158 


Fri 20041001 4:46 PM
Hello;
[quote="On Thu, 30 Sep 2004, J.C. Yoon"] Dear Professor Grunewald,
Recently, I have noticed that you have cited E158 paper
"Observation of Parity Nonconservation in Moller Scattering" in your reprint.
However, there is one thing I could not figure out in E158 paper. As
long as I know, the helicity of a massive particle is not definite,
since we can always find a boosted frame of reference in which the
helicity is the opposite. Therefore, E158 measurment of helicity of
electron or muons is only that of laboratory frame and it implies Lorentz violation.
I would like to appreciate if you can explain this issue.
I sincerely apologize for your time and effort if you find it unworthy
of your attention.
I am looking forward to hearing from you.[/quote]
Independent of E158, the last step in your reasoning is invalid:
[quote="J.C. Yoon"] only that of laboratory frame and it implies Lorentz violation.[/quote]
In physics, lots of things are measured in a framedependent way, e.g., velocities. Framedependence does not imply Lorentz violation.
In the highenergy limit, helicity becomes equal to chirality which the weak interaction depends on. Hence both terms are often used synonymously. The E158 result is a function of the underlying weak physics, and the kinematic setup (energies etc.). The kinematic setup is faremdependent (the lab system), but from the measurement result a frameindependent intrinsic property of the particles involved is derived.
Best regards
Martin Grunewald

Martin W. Gruenewald email: Martin.Grunewald@cern.ch
http://cern.ch/Martin.Grunewald
Room 115, Department of Experimental Physics, Faculty of Science,
University College Dublin, Belfield, Dublin 4, Ireland
Phone: ++353 1 716 2210, 2217 Fax: ++353 1 283 7275
CERN EP/L3 322A13, CH1211 Geneva 23, Switzerland
Phone: ++41 22 76 70641, 79927, 74477 Fax: ++41 22 78 28923 

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jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Sat Oct 21, 2006 2:48 pm Post subject: RE: Parity Violation at E158 


Sat 20041002 12:08 AM
Dear Professor Gruenewald,
Thanks for you reply and time.
First, I couldn't agree more with your point about Lorentz violation, but I think I was not clear about that point.
Let us say we have physical observations of lefthanded and righthanded electrons in the lab frame. Since it is massive, both could be observed as that of righthanded electron from a certain frame of refence. Therefore, our analysis is based on a specific frame of reference does not hold in other frame and this explanation violates Lorentz invariance, since it is not a frameindependent intrinsic property.
The covariance of helicity may be found in the Bjorken and Drell, but I believe its assumption that spin transform as fourvector is of question.
Let us consider a particle with spin and momentum. If we boost a frame faster than this particle, will it change its spin? If we think of spin as rotation, then the answer is no and we may refer to peskin & shroeder p47. The property of spin is well understood as an angular momentum, if it is true that spin transforms as fourvector, it means that our understanding the spin as the analogy of angular momentum is incorrect, since transform does not conserve the angular momentum.
Therefore, it is doubtful that spin transforms as fourvectors.
Thanks,
J.C. Yoon 

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Martin Gruenewald
Joined: 28 Sep 2006 Posts: 5

Posted: Sat Oct 21, 2006 2:50 pm Post subject: RE: Parity Violation at E158 


Mon 20041115 9:56 PM
Hello;
I think I answered it in my last email:
[quote="On Fri, 12 Nov 2004, J.C. Yoon"] Dear Professor Grunewald,
I am afraid if you find this email annoying and sincerely apologize
for bothering you, but I would like to let you know I am still waiting
for you response.
Let rephrase my point.
The lefthandedness and righthandedness of massive particle is
indefinte since it violates Lorentz invariance and do does the
theoretical explanation for E158.[/quote]
A quantity being frame dependent does not mean violation of Lorentz invariance. E158 measured a combination of coupling constants which is frame independent, however, using a set up in a laboratory with kinematics which are frame dependent as they are set up in the laboratory frame.
Best regards
Martin Grunewald 

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jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Sat Oct 21, 2006 2:51 pm Post subject: RE: Parity Violation at E158 


Tue 20041116 5:55 AM
Dear Professor Gruenewald,
I would like to appreciate your kind response but it could not resolve the problem I had and I sent you anthor email for more help.
Please forgive me for taking up your precious time.
If you allow me, I would like to explain what I think in more detail.
The weak interactions was originally understood as having a different
structure(chirality: 1 \pm \gamma_5) than the em interactions by Fermi and others in early stage(Feynman and GellMann, PR 109 (1958) 193, Sudarshan and Marshak, PR 109 (1958) 1860). However, the Standard Model suggested that, instead of interpreting this as a property of interaction structure, we should interpret this as interaction of the left or righthanded massive fermions.
Here I am trying to argue that the subtle distinction between these seeminglyalternative interpretations are quite significant and something that cannot be compromised.
First, the massless limit approximation in massive fermion in Standard Model is Lorentz violating. We can prove this by starting with the exact Dirac solution in the rest frame and boost it and make approximation(as you know, we can find this in usual introduction of field theory book such Peskin and Shroeder) and now boost this approximated one back to the rest frame, where we find that the exact ones cannot be achieved by Lorentz transformation of the approximated one. Therefore, for massive fermion, there is no purely left or righthanded states without Lorentz violation. In E158 experiments, no matter how high the momentum is, we should not neglect the depressed component. This is the point people think of the chirality of structure and say that it would not matter since even if we have the other components, the interactions does not associate with it. As matter of fact, the calculation of Lorentz invariant observation should be done with the exact solution of Dirac equation in the rest frame in stead of the approximated one in the boosted frame, but the calculation should be the same due to the structure of weak interactions. However, it is still incorrect to accept the property of fermion state conflicting with Dirac equation and Lorentz invariance just because of the structure of interactions. Also, the calculation of Lorentz invariant observation should be done with the exact solution of Dirac equation in the rest frame in stead of the approximated one in the boosted frame.
Second, it is, therefore, correct to interpret weak interaction as one with a certain structure than one of massive fermion with definite helicity. Though it looks the same, there is quite sharp distinction between these two interpretations. If the weak interactions have a certain structure different from the em interactions and this indicates the difference in the fundamental symmetry of parity, then these two interactions are fundamentally different from each other so that the unification of electroweak interaction is contradicted.
I believe this would be a good place to stop and ask your opinion before stepping in more difficult questions.
Thanks,
J.C. Yoon 

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Martin Gruenewald
Joined: 28 Sep 2006 Posts: 5

Posted: Sat Oct 21, 2006 3:24 pm Post subject: RE: Parity Violation at E158 


Wed 20041124 11:30 PM
Hi;
[quote="On Mon, 15 Nov 2004, J.C. Yoon"] Dear Professor Gruenewald,
I would like to appreciate your kind response but it could not resolve
the problem I had and I sent you anthor email for more help.
Please forgive me for taking up your precious time.
If you allow me, I would like to explain what I think in more detail.
The weak interactions was originally understood as having a different
structure(chirality: 1 \pm \gamma_5) than the em interactions by Fermi
and others in early stage(Feynman and GellMann, PR 109 (1958) 193,
Sudarshan and Marshak, PR 109 (1958) 1860). However, the Standard
Model suggested that, instead of interpreting this as a property of
interaction structure, we should interpret this as interaction of the
left or righthanded massive fermions.[/quote]
No: the true structure of ew interactions is 1+gamma(5). In the ultra relativistic limit, helicity (projection of spin along momentum) and chirality agree. Thus, speaking of the weak interaction discriminating
left and righthanded particles is just an approximation, the correct thing to say is it discriminates chirality +1 and 1 particles.
However, left and righthanded is easier to understand. Thus the whole problem is simply one of using a not quite precise but intuitive picture.
The true mathematics of the SM uses chirality. Don't take such conceptual pictures to the extreme, what counts in the end is not the (fuzzy) picture but the mathematical structure.
Best regards
Martin Grunewald 

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jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Sun Oct 22, 2006 12:00 am Post subject: RE: Parity Violation at E158 


Thu 20041125 2:43 AM
Dear Professor Gruenewald,
Thanks for your kind response and time.
I am afraid that I am still inquisitive about some aspects of your argument. Please forgive me for carrying this argument further and I would like to appreciate if you could share your opinion on the following points.
[quote="On Wednesday, November 24, 2004 6:30 AM, Martin Gruenewald"] the true structure of ew interactions is 1+gamma(5).[/quote]
I am a little bit confused here.
If 1+gamma(5) is true structure for em interactions, then we do not need to observe this in the ultrarelativistic limit, since regardless of its momentum or helicity, this structure should be valid as it chooses the right chirality.
The critical issue here is whether the massive fermions are the eigenstates of chirality. Unless we use the approximation, there is no massive fermion state purely with one chirality. Also, this chirality is experimentally determined from the measurement of the helicity.
Otherwise, I am not aware how we measure the chirality of particle.
Thanks,
J.C. Yoon 

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Martin Gruenewald
Joined: 28 Sep 2006 Posts: 5

Posted: Sun Oct 22, 2006 12:02 am Post subject: RE: Parity Violation at E158 


Thu 20050106 4:33 AM
Hi;
I think I did not answer this one so far...
[quote="On Wed, 24 Nov 2004, J.C. Yoon"] Dear Professor Gruenewald,
Thanks for your kind response and time.
I am afraid that I am still inquisitive about some aspects of your
argument. Please forgive me for carrying this argument further and I
would like to appreciate if you could share your opinion on the
following points.
>the true structure of ew interactions is 1+gamma(5).
I am a little bit confused here.
If 1+gamma(5) is true structure for em interactions, then we do not
need to observe this in the ultrarelativistic limit, since regardless
of its momentum or helicity, this structure should be valid as it
chooses the right chirality.[/quote]
The reason to talk about helicity (left and righthandedness defined as projection of spin along momentum direction) is simply that handedness has a nice, even classical meaning (namely handedness). In contrast,
1+gamma(5) does not have such a nice intuitive explanation, just the
definition of +/ chirality. However, in the limit of high energy both become the same, hence one is carrying over this concept. Just take it as fuzzy language, calculations use chirality, not helicity. However, the `mistake' you make using helicity instead of chirality vanishes for highenergies, thus there is some justification to use it there as well (similar as to use Newtonian gravity to calculate satellite orbits, rather than full blown general relativity).
Best regards
Martin Grunewald 

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jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Sun Oct 22, 2006 12:03 am Post subject: RE: Parity Violation at E158 


Tue 20050215 8:42 AM
Dear Professor Gruenewald,
I am sorry for my late reply and appreciate your kind explanation.
Please forgive my further argumentation and feel free to pinpoint the flaw of my argument.
[quote="On Wednesday, January 05, 2005 11:33 AM, Martin Gruenewald"] However, the `mistake' you make using helicity instead of chirality
vanishes for highenergies, thus there is some justification to use it
there as well (similar as to use Newtonian gravity to calculate
satellite orbits, rather than full blown general relativity).[/quote]
First, using helicity instead of chirality is not a mistake.
The massive fermion satisfying the Dirac equation is always represented with two chiralities.
In the high energy limit, one of them may look smaller but in the rest frame they are even.
While we have an accurate calculation available for the rest frame, there is no good reason to use the description of physics in the approximation of the high energy limit, especially when the physical observation(interactions) is expected to be Lorentz invariant. Since we have two nonvanishing Weyl spinors in the rest frame, it is rather "correct" to use helicity than chirality for massive fermion as the justification of using chirality fails.
Second, the approximation employed in high eneryg limit violates Lorentz invariance.
In the high energy limit, one of the Weyl spinor gets smaller, but if we neglect this term, we won't be able to obtain the rest frame Dirac solution by taking Lorentz transformation on this approximated one with one chirality.
Therefore, this approximation violates Lorentz invariance.
A massive fermion can NOT be described by one "chirality" without this approximation.
A ball can be successfully describe by classical mechanics assuming this ball as pointlike particle. However, this approximation can NOT be used to justify to claim that the ball is a point. No matter how a massive fermion behaves like a massless one, we can NOT claim its fundamental property is that of massless one.
Thanks,
J.C. Yoon 

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Martin Gruenewald
Joined: 28 Sep 2006 Posts: 5

Posted: Sun Oct 22, 2006 12:05 am Post subject: RE: Parity Violation at E158 


Sat 20050326 7:15 AM
Hi;
I think by now we have very much deviated from the original problem.
An approximation is an approximation, and if one leaves its range of applicability (e.g., E>>m in this case), then the approximation no longer works. Still, one keeps and uses the approximation if one happens to be in the range wehere it is valid.
In the high energy limit chiralityhelicity.
It is similar to LorntzT versus GalileiT: every engineer uses GT (and buildings still stand and machines still work), even though Lorentz T is the correct way of doing things.
Best regards
Martin 

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jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Sun Oct 22, 2006 12:07 am Post subject: RE: Parity Violation at E158 


Sat 20050326 9:31 AM
Dear Martin Gruenewald,
It is my pleasure to have your opinion again.
I am still worried that you may be bothered with my emails, but hopefully, I wish you would enjoy these correspondences as much as I do.
Yes, it is quite digressed from where I started with.
Maybe, it is because I have been obscure about the ultimate point I would like to make.
Here is the point.
"The unification of electroweak interactions is only valid under an approximation that violates Lorentz invariance."
I agree with you that an approximation is an approximation and GT is only approximately valid, but incorrect, rigorously speaking.
So is the unification of electroweak interactions and it is only approximately valid, but it fails to be correct, rigorously speaking.
If it does not require high accuracy, GT or any approximations are fine.
But, if we are dealing with the fundamental property of nature, we should not rely on any approximation to make our judgment.
Thanks,
J.C. Yoon 

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