jcyoon
Joined: 08 Aug 2006 Posts: 213

Posted: Sun Jul 26, 2009 6:42 pm Post subject: Relative Spin Polarization of Parity Violation 


Dear Professors Weinberg and Glashow,
It has been a long time since we exchanged our opinions about whether the Standard Model is rigorously Lorentz invariant, especially for massive fermions such as in the SLAC E158 experiments.
Since many physicists still think that my argument is somehow flawed, I would like you to confirm and endorse my claim that the Standard Model is based on the Lorentzviolating approximation.
One of the reasons that this issue has not been clearly resolved is that no exact calculation of the parityviolating asymmetry was available. As Professor Stanley J. Brodsky at SLAC suggested, I performed an exact calculation of the parityviolating asymmetry for SLAC E158 and SLD following the original expression of the spin projection operator in H.A. Tolhoek, Rev. Mod. Phys. 28 (1956) 277. The calculation result is quantitatively consistent with the approximate SLAC E158 and SLD calculation, but it is explicitly Lorentz invariant, at least, along the z direction, while in the approximate one the spin polarization and momentum under parity is ambiguous and thus misleading to interpret the asymmetry in terms of helicity. From the explicit expression of the parityviolating asymmetry,
A_{PV} ~ +(vz_{incoming}  vz_{target}),
we can see the sign of parityviolating term measured in SLAC E158 depends not on the helicity of incoming electron alone, but on the relative velocity between incoming and target electrons, as well as the spin polarization direction. On the contrary, if the helicity of incoming electron were responsible for parity violation as the Standard Model presumes, the parityviolating asymmetry should be in the following form,
A_{PV} ~ +(vz_{incoming})
which is consistent with the exact calculation only when the target electron is at rest. Therefore, the mathematical calculation proves that the interpretation of the parity violating asymmetry in terms of helicity, the premise of the Standard Model, is qualitatively limited and inconsistent with the exact analysis.
Please take a look at the details of the calculation in http://uk.arxiv.org/abs/0811.3700 and correct me if I am mistaken in claiming that the SLAC E158 and SLD asymmetry measurements is Lorentz invariant according to its exact calculation interpreting the asymmetry in terms of relative spin polarization, but its Standard Model interpretation as helicity asymmetry is not Lorentz invariant since helicity and thus the asymmetry are variant under the Lorentz transformations.
Also, I have come across a physicist arguing that the approximation is still valid since it is quantitatively consistent with the exact calculation. In my opinion, it is inappropriate to justify any approximation that qualitatively distorts the original physical property of the observables. Would you agree with him upholding such an approximation to claim that the Standard Model is still valid for the fundamental and rigorous unification of electroweak interactions? Or if you have more cogent and reasonable arguments, please let me know.
You may think it is within your discretion not to respond to my request for your academic opinion. But I believe you are obliged to respond on behalf of the public and all the physicists including me who hold you in high esteem. And there should be a limit on academic freedom, especially if it is to sustain the public funding while you are well aware of the critical flaw in the science project.
Sincerely yours,
J.C. Yoon 
