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jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Mon Oct 23, 2006 12:53 pm    Post subject: Parity Violation at E158 lance@slac.stanford.edu Fri 2004-10-01 8:51 AM Dear Professor Dixon, 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
Lance Dixon

Joined: 28 Sep 2006
Posts: 4

 Posted: Mon Oct 23, 2006 12:55 pm    Post subject: Re: Parity Violation at E158 Sun 2004-10-03 12:30 AM Dear Dr. Yoon, [quote="J.C. Yoon"] 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.[/quote] It is true that for a massive particle, it is possible to boost to a frame where the motion of the particle is in the opposite direction from the unboosted frame. In the new frame, the spin angular momentum can point in the opposite direction from the direction of motion, whereas previously it pointed in the same direction. That does not mean, however, that any of the E158 measurements imply Lorentz violation. Indeed, they can be cast in terms of expectation values of Lorentz-invariant observables. The one our paper was concerned with, the transversely polarized single-spin asymmetry, can be written as < \eps_{\mu_1\mu_2\mu_3\mu_4} k_{e_1}^{\mu_1} k_{e_1'}^{\mu_2} k_{e_2}^{\mu_3} n^{\mu_4} > where k_{e_1} and k_{e_1'} are incoming and outgoing electron momenta, k_{e_2} is the target electron momentum, and n is the spin vector for the incoming electron, which should satisfy n_\mu k_{e_1}^\mu = 0. All of these are Lorentz-covariant 4-vectors. Contracting them with the Lorentz-covariant Levi-Civita tensor \eps gives a Lorentz-invariant quantity, which can be evaluated in any frame. In the target rest frame it becomes < S_e . (k_{e} x k_{e'}) > (see our eq. (1)). E158 also measures a longitudinally polarized, parity-violating, asymmetry. This can be stated even more simply than the above, as an expectation value of < n_\mu k_{e_2}^\mu > This is simpler to evaluate first in the center-of-mass frame, where it is easier to see that it is proportional to the right-left asymmetry. Boosting to the lab frame, the component of the spin along the beam direction doesn't change, and it still represents such an asymmetry. Sometimes the term "helicity" is used as a slightly sloppy shorthand for something Lorentz invariant, like n_\mu k_{e_2}^\mu. For "reasonable" boosts (but not all, as you realize), the two quantities will have the same sign. I hope that answers your question. Best Regards, Lance
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Mon Oct 23, 2006 12:57 pm    Post subject: RE: Parity Violation at E158 Sun 2004-10-03 1:38 AM Dear Professor Dixon, I would like to appreciate your kind answer and time. I agree in most of frame the observation of E158 is valid and it represents a certain asymmetry, but I am concerned with a theoretical aspects. This may be argued by the following. 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. I believe that this is quite a reasonable doubt to the theoretical approximation of massless limit, since the fundamentality of helicity is subjected to this approximation. In the massless limit, the helicity is a good quantum number but not if massive and the helicity definition is not even clear in rest frame. This approximation changes not-a-good-quantum-number into a good quantum number. As long as the theory is limited by this aspect, it would be rather natural to investigate and view the spin dependency of interactions, which may lead us to new physics. I would like to arppreciate if you can help me on this issue. Thanks, J.C. Yoon
Lance Dixon

Joined: 28 Sep 2006
Posts: 4

 Posted: Mon Oct 23, 2006 12:59 pm    Post subject: RE: Parity Violation at E158 Sun 2004-10-03 1:48 AM Dear Dr. Yoon, [quote="J.C. Yoon"] 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] I guess you did not actually read my reply, in which I explained to you how to recast the E158 measurements in terms of expectation values of frame-independent quantities? [quote="J.C. Yoon"] I believe that this is quite a reasonable doubt to the theoretical approximation of massless limit, since the fundamentality of helicity is subjected to this approximation. In the massless limit, the helicity is a good quantum number but not if massive and the helicity definition is not even clear in rest frame. This approximation changes not-a-good-quantum-number into a good quantum number.[/quote] There are plenty of other examples of approximations turning not-a-good-quantum numbers into good quantum numbers (quark masses & SU(2) or SU(3), parity invariance neglecting the weak interactions, etc.). I don't think that casts any doubt on the possibility of taking the massless limit. (It is trickier than some others, due to additional collinear divergences, but still can be done consistently.) [quote="J.C. Yoon"] it would be rather natural to investigate and view the spin dependency of interactions, which may lead us to new physics.[/quote] That's what E158 is hoping too. Best Regards, Lance
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Mon Oct 23, 2006 1:01 pm    Post subject: RE: Parity Violation at E158 Sun 2004-10-03 2:59 AM Dear Professor Dixon, It looks like I did not understand your point in the following. I would like to apology for this and appreciate if you could explain this point again if I have mistaken. [quote="On Saturday, October 02, 2004 9:48 AM, Lance Dixon"] E158 also measures a longitudinally polarized, parity-violating, asymmetry. This can be stated even more simply than the above, as an expectation value of < n_\mu k_{e_2}^\mu > This is simpler to evaluate first in the center-of-mass frame, where it is easier to see that it is proportional to the right-left asymmetry. Boosting to the lab frame, the component of the spin along the beam direction doesn't change, and it still represents such an asymmetry.[/quote] Though this measument is valid in the CM and the lab frame, I thought this is only valid within "reasonable" boosts and thus theoretically there exist some frames the analysis do not hold. Thanks for your patience and time. Thanks, J.C. Yoon
Lance Dixon

Joined: 28 Sep 2006
Posts: 4

 Posted: Mon Oct 23, 2006 1:02 pm    Post subject: RE: Parity Violation at E158 Sun 2004-10-03 3:20 AM Dear Dr. Yoon, [quote="J.C. Yoon"] >E158 also measures a longitudinally polarized, parity-violating, >asymmetry. This can be stated even more simply than the above, >as an expectation value of >< n_\mu k_{e_2}^\mu > >This is simpler to evaluate first in the center-of-mass frame, >where it is easier to see that it is proportional to the right-left >asymmetry. Boosting to the lab frame, the component of the spin along >the beam direction doesn't change, and it still represents such an >asymmetry. Though this measument is valid in the CM and the lab frame, I thought this is only valid within "reasonable" boosts and thus theoretically there exist some frames the analysis do not hold.[/quote] The _measurement_ is valid in all frames, because it is of a Lorentz-invariant observable. The _interpretation_ as a (right - left)/(right + left) asymmetry is valid in "reasonable" frames. But a very large boost along the beam axis can cause the beam electron as well as the target electron to be travelling "backwards along the beam axis, and therefore switch the helicity of the beam electron. The _interpretation_ of the quantity would then be of a (left - right)/(left + right) asymmetry. -Lance
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Mon Oct 23, 2006 1:21 pm    Post subject: RE: Parity Violation at E158 Thu 2004-10-07 3:40 AM Dear Professor Dixon, I am sorry for late reply. I agree with your explanation, but I still find this theoretical explanation(_interpretation_) unsatisfactory. This explains a Lorentz-invariant measurement as a Lorentz violating quantity while it does not provide the exact theoretical prediction so that we could estimate how accurate this approximation is. Thanks, J.C. Yoon
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Mon Oct 23, 2006 1:28 pm    Post subject: RE: Parity Violation at E158 Sat 2004-11-13 8:47 AM Dear Professor Dixon, 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. I would be grateful if you can share your opinion with me. Thanks, J.C. Yoon
Lance Dixon

Joined: 28 Sep 2006
Posts: 4

 Posted: Mon Oct 23, 2006 1:29 pm    Post subject: RE: Parity Violation at E158 Sun 2004-11-14 2:01 AM Dear Dr. Yoon, I'm sorry, I did not realize that your e-mail required a reply. You said you agreed with my explanation, but found it unsatisfactory. All I can do is apologize, and hope that you will be able to write down the exact, mass-dependent, Lorentz-invariant description of the experiment to your own satisfaction. It should not be very difficult to do, actually it was probably done by Barut and Fronsdal, or DeRaad and Ng (in the reference list of our paper). Best Regards, Lance
jcyoon

Joined: 08 Aug 2006
Posts: 213

 Posted: Mon Oct 23, 2006 1:31 pm    Post subject: RE: Parity Violation at E158 Tue 2004-11-16 5:55 AM Dear Professor Dixon, I would like to appreciate you kind response, but I think there are somethings I need to make clear. Please forgive me for taking up your precious time. If you allow me, I would like to bring up more subtle point here. 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 and also Barut and Fronsdal and DeRaad and Ng). 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
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