View previous topic :: View next topic 
Author 
Message 
jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Tue Oct 24, 2006 12:14 pm Post subject: Parity Violation at E158 


Fri 20041001 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 

Back to top 


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 20041001 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 fourvectors.
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 

Back to top 


jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Tue Oct 24, 2006 12:19 pm Post subject: RE: Parity Violation at E158 


Sat 20041002 12:08 AM
Dear Professor Brodsky,
Thanks you for your reply and time.
It looks like the point is whether $s^\mu$ transforms as fourvectors.
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 $s^\mu$ transforms as fourvectors.
I would like to appreciate your response and I will be looking forward to hearing from you.
Thanks,
J.C. Yoon 

Back to top 


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 20041002 12:34 AM
Dear J.C. Yoon,
[quote="J.C. Yoon"] Therefore, it is doubtful that $s^\mu$ transforms as fourvectors.[/quote]
Please let me write below what I think:
When we write $s^\mu$, it means that $s^\mu$ is a fourvector which
transforms as a fourvector. 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 

Back to top 


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 20041002 1:13 AM
Dear J.C.,
I agree with Dae Sung.
Best regards,
Stan 

Back to top 


jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Tue Oct 24, 2006 12:29 pm Post subject: RE: Parity Violation at E158 


Sat 20041002 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 righthandedness change into the lefthandedness 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 Lorentzinvariant but covariant.
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.
Thanks,
J.C. Yoon 

Back to top 


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 20041002 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 righthandedness change into the lefthandedness 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 Lorentzinvariant but covariant.
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.[/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 fourvector.
Best regards,
Stan 

Back to top 


jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Tue Oct 24, 2006 12:45 pm Post subject: RE: Parity Violation at E158 


Sat 20041002 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 righthandedness framedenpendent and it
is still consistent since it keeps helicity projector Lorentz scalar due to $\gamma^\mu$.
Thanks,
J.C. Yoon 

Back to top 


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 20041002 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 

Back to top 


jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Tue Oct 24, 2006 12:49 pm Post subject: RE: Parity Violation at E158 


Sun 20041003 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 

Back to top 


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 20041003 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/hepph/pdf/0008/0008055.pdf
Best regards,
Stan 

Back to top 


jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Tue Oct 24, 2006 12:51 pm Post subject: RE: Parity Violation at E158 


Thu 20041007 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 Lorentzviolating theoretical
explanation of leftright asymmetry since this could be observed as rightright 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 

Back to top 


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 20041007 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 Lorentzviolating theoretical explanation of leftright asymmetry since this could be observed as rightright 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 

Back to top 


jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Tue Oct 24, 2006 12:54 pm Post subject: RE: Parity Violation at E158 


Wed 20050601 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/hepph/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 

Back to top 


