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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 2004-10-01 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
Martin Gruenewald

Joined: 28 Sep 2006
Posts: 5

 Posted: Sat Oct 21, 2006 2:46 pm    Post subject: Re: Parity Violation at E158 Fri 2004-10-01 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 E-158, 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 frame-dependent way, e.g., velocities. Frame-dependence does not imply Lorentz violation. In the high-energy limit, helicity becomes equal to chirality which the weak interaction depends on. Hence both terms are often used synonymously. The E-158 result is a function of the underlying weak physics, and the kinematic set-up (energies etc.). The kinematic setup is farem-dependent (the lab system), but from the measurement result a frame-independent intrinsic property of the particles involved is derived. Best regards Martin Grunewald -- Martin W. Gruenewald e-mail: 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 32-2A13, CH-1211 Geneva 23, Switzerland Phone: ++41 22 76 70641, 79927, 74477 Fax: ++41 22 78 28923
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Sat Oct 21, 2006 2:48 pm    Post subject: RE: Parity Violation at E158 Sat 2004-10-02 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 left-handed and right-handed electrons in the lab frame. Since it is massive, both could be observed as that of right-handed 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 frame-independent intrinsic property. The covariance of helicity may be found in the Bjorken and Drell, but I believe its assumption that spin transform as four-vector 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 four-vector, 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 four-vectors. Thanks, J.C. Yoon
Martin Gruenewald

Joined: 28 Sep 2006
Posts: 5

 Posted: Sat Oct 21, 2006 2:50 pm    Post subject: RE: Parity Violation at E158 Mon 2004-11-15 9:56 PM Hello; I think I answered it in my last e-mail: [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 left-handedness and right-handedness 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
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Sat Oct 21, 2006 2:51 pm    Post subject: RE: Parity Violation at E158 Tue 2004-11-16 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 Gell-Mann, 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 right-handed massive fermions. Here I am trying to argue that the subtle distinction between these seemingly-alternative 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 right-handed 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
Martin Gruenewald

Joined: 28 Sep 2006
Posts: 5

 Posted: Sat Oct 21, 2006 3:24 pm    Post subject: RE: Parity Violation at E158 Wed 2004-11-24 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 Gell-Mann, 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 right-handed 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 right-handed particles is just an approximation, the correct thing to say is it discriminates chirality +1 and -1 particles. However, left- and right-handed 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
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Sun Oct 22, 2006 12:00 am    Post subject: RE: Parity Violation at E158 Thu 2004-11-25 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 ultra-relativistic 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
Martin Gruenewald

Joined: 28 Sep 2006
Posts: 5

 Posted: Sun Oct 22, 2006 12:02 am    Post subject: RE: Parity Violation at E158 Thu 2005-01-06 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 ultra-relativistic 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 right-handedness 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 high-energies, 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
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Sun Oct 22, 2006 12:03 am    Post subject: RE: Parity Violation at E158 Tue 2005-02-15 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 high-energies, 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
Martin Gruenewald

Joined: 28 Sep 2006
Posts: 5

 Posted: Sun Oct 22, 2006 12:05 am    Post subject: RE: Parity Violation at E158 Sat 2005-03-26 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 chirality-helicity. It is similar to Lorntz-T versus Galilei-T: 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
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Sun Oct 22, 2006 12:07 am    Post subject: RE: Parity Violation at E158 Sat 2005-03-26 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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