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jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Tue Oct 24, 2006 12:14 pm    Post subject: Parity Violation at E158 Fri 2004-10-01 8:51 AM sjbth@slac.stanford.edu Dear Professor Brodsky, 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
Stanley J. Brodsky

Joined: 28 Sep 2006
Posts: 6

 Posted: Tue Oct 24, 2006 12:17 pm    Post subject: RE: Parity Violation at E158 Fri 2004-10-01 3:22 PM Dear J.C., 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. JC: Therefore, E158 measurement 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. Sjb: The helicity is the spin projection of the particle in the direction of momentum the particle. It can be defined covariantly so it has the same value in any Lorentz frame. The covariant definition is given in the Bjorken and Drell book and slide 8 from: http://urhic.phys.jyu.fi/JSS04/Heppelmann/3DiracSpin.ppt. Note that both $s^\mu$ and $p^\mu$ transform as four-vectors. I am sending this correspondence to my colleague Dae Sung Hwang in case he can add more clarification. Hope this response is helpful. Best regards, Stan
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Tue Oct 24, 2006 12:19 pm    Post subject: RE: Parity Violation at E158 Sat 2004-10-02 12:08 AM Dear Professor Brodsky, Thanks you for your reply and time. It looks like the point is whether $s^\mu$ transforms as four-vectors. 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 $s^\mu$ transforms as four-vectors. I would like to appreciate your response and I will be looking forward to hearing from you. Thanks, J.C. Yoon
Dae Sung Hwang

Joined: 24 Oct 2006
Posts: 1

 Posted: Tue Oct 24, 2006 12:26 pm    Post subject: RE: Parity Violation at E158 Sat 2004-10-02 12:34 AM Dear J.C. Yoon, [quote="J.C. Yoon"] Therefore, it is doubtful that $s^\mu$ transforms as four-vectors.[/quote] Please let me write below what I think: When we write $s^\mu$, it means that $s^\mu$ is a four-vector which transforms as a four-vector. As one sees in page 282 of Bjorken and Drell Relativistic Quantum Mechanics, $s^\mu$ is $(0 , {\hat s})$ in the rest frame of the particle. Then, $s^\mu$ in another frame is obtained by Lorentz transforming $(0 , {\hat s})$ to this another frame from the rest frame of the particle. I hope that what I wrote above is useful. If it is not clear, please let me know. Sincerely, Dae Sung Hwang
Stanley J. Brodsky

Joined: 28 Sep 2006
Posts: 6

 Posted: Tue Oct 24, 2006 12:28 pm    Post subject: RE: Parity Violation at E158 Sat 2004-10-02 1:13 AM Dear J.C., I agree with Dae Sung. Best regards, Stan
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Tue Oct 24, 2006 12:29 pm    Post subject: RE: Parity Violation at E158 Sat 2004-10-02 3:40 AM Dear Professor Brodsky, I made a mistake in understanding the notation of $s^{mu}$ in the Bjorken and Drell. Thank Dae Sung for correcting my mistake and I agree with him. However, my point is still valid. Let us look at Eq.(7.94) page 141 in Bjorken and Drell. We can see the right-handedness change into the left-handedness as we boost a frame of reference so that it changes the sign of $\beta_{i} = \vec p_i \over E_i$. Therefore, it is not Lorentz-invariant but covariant. 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. Thanks, J.C. Yoon
Stanley J. Brodsky

Joined: 28 Sep 2006
Posts: 6

 Posted: Tue Oct 24, 2006 12:44 pm    Post subject: RE: Parity Violation at E158 Sat 2004-10-02 6:05 AM Dear JC: [quote="J.C. Yoon"] I made a mistake in understanding the notation of $s^{mu}$ in the Bjorken and Drell. Thank Dae Sung for correcting my mistake and I agree with him. However, my point is still valid. Let us look at Eq.(7.94) page 141 in Bjorken and Drell. We can see the right-handedness change into the left-handedness as we boost a frame of reference so that it changes the sign of $\beta_{i} = \vec p_i \over E_i$. Therefore, it is not Lorentz-invariant but covariant. 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.[/quote] Sjb: The helicity projectors $$\Sigma_\pm = {1\over 2}{1 \pm s^\mu \gamma^\mu \gamma_5}$$ are Lorentz scalars formed from the dot product of $s^\mu$ with $\gamma^\mu \gamma_5$ which also transforms as a four-vector. Best regards, Stan
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Tue Oct 24, 2006 12:45 pm    Post subject: RE: Parity Violation at E158 Sat 2004-10-02 7:22 AM Dear Professor Brodsky, Thanks for your patience with my questions. I agree that the helicity projector is Lorentz scalar, since $s^\mu \gamma^\mu \gamma_5$ is a scalar as a production of vector, vector and scalar. But, the definition of helicity is not exactly up to this projector, but determined from whether spin orientation is parallel or antiparallel to momentum, which makes left- and right-handedness frame-denpendent and it is still consistent since it keeps helicity projector Lorentz scalar due to $\gamma^\mu$. Thanks, J.C. Yoon
Stanley J. Brodsky

Joined: 28 Sep 2006
Posts: 6

 Posted: Tue Oct 24, 2006 12:46 pm    Post subject: RE: Parity Violation at E158 Sat 2004-10-02 7:35 AM Dear JC, You may be confusing chirality and helicity. You need to use the helicity projectors for massive particles. Best regards, Stan
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Tue Oct 24, 2006 12:49 pm    Post subject: RE: Parity Violation at E158 Sun 2004-10-03 1:38 AM Dear Professor Brodsky, I may be confusing with chirality and helicity. I would like to apologize for this confusion and let me clear these things up. Chirality operator: ${1\over 2}{1 \pm \gamma_5}$ Helicity operator: {1\over 2}{1 \pm p^{\hat} \Sigma} Spin projection operator $$\Sigma_\pm = {1\over 2}{1 \pm s^\mu \gamma^\mu \gamma_5}$$ I agree we need helicity operator with a massive particle and, in fact, my argument is mainly concerned with the difference between chirality and helicity questioning whether the approximation of helicity to chirality in the massless limit is theoretically impeccable. Thanks, J.C. Yoon
Stanley J. Brodsky

Joined: 28 Sep 2006
Posts: 6

 Posted: Tue Oct 24, 2006 12:50 pm    Post subject: RE: Parity Violation at E158 Sun 2004-10-03 5:00 AM Dear J.C., I am beginning to see your point. I was confusing the helicity operator with the spin operator which is a Lorentz scalar. As you note, the helicity operator is defined (e.g., to classify Dirac spinors) in a frame like the CM. You would like to have a covariant definition. I had thought that people always use the spin operator to do this. Is there a problem with this? Maybe Dae Sung can clarify. Here is a paper which might be useful. http://arxiv.org/PS_cache/hep-ph/pdf/0008/0008055.pdf Best regards, Stan
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Tue Oct 24, 2006 12:51 pm    Post subject: RE: Parity Violation at E158 Thu 2004-10-07 3:54 AM Dear Professor Brodsky, I am sorry for the late reply. I guess that you would agree that the reason the spin operator was brought up is due to the shortcomings of the helicity operator. For a massive particle, its definition, for example, is ambiguous in the rest frame and depends on the frame of reference. Unfortunately, I believe people used rather the helicity than the covariant spin operators in their measurement and theory. Therefore, we have a Lorentz-violating theoretical explanation of left-right asymmetry since this could be observed as right-right asymmetry in a boosted frame. And it is difficult to be justified as an approximation since theory does not provide the exact prediction so that we could estimate how accurate this approximation is. Thanks, J.C. Yoon
Stanley J. Brodsky

Joined: 28 Sep 2006
Posts: 6

 Posted: Tue Oct 24, 2006 12:53 pm    Post subject: RE: Parity Violation at E158 Thu 2004-10-07 7:41 AM Dear J. C., [quote="J.C. Yoon"] I guess that you would agree that the reason the spin operator was brought up is due to the shortcomings of the helicity operator. For a massive particle, its definition, for example, is ambiguous in the rest frame and depends on the frame of reference. Unfortunately, I believe people used rather the helicity than the covariant spin operators in their measurement and theory. Therefore, we have a Lorentz-violating theoretical explanation of left-right asymmetry since this could be observed as right-right asymmetry in a boosted frame. And it is difficult to be justified as an approximation since theory does not provide the exact prediction so that we could estimate how accurate this approximation is.[/quote] Sjb: It seems like a good idea for you to repeat the calculation for E158 using the spin projection method and quantify any difference. Best regards, Stan
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Tue Oct 24, 2006 12:54 pm    Post subject: RE: Parity Violation at E158 Wed 2005-06-01 5:09 AM Dear Professor Brodsky, Recently, I have posted a preprint that is related to our previous discussion. "Lorentz violation of the standard model"( http://arxiv.org/abs/hep-ph/0502142 ). It is quite frustrating to argue against what most people think, but I could not find any fallacy of scientific method in my argument. Though I know it sounds outrageous and it may waste your time, I would like to ask you a favor to read this preprint and let me know your opinion. If you could point out where my argument fails so that I could stop this nonsense, I will deeply appreciate it with all respect. In advance, I would like to apologize any time you would waste if it is just a nonsense. Thanks, J.C. Yoon
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