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And if so, can we observe a difference in the electron scattering cross section with transversely polarized VS longitudinally polarized protons?

P.S. Let me make my question more precise. Consider the charge shape of the proton. In the rest frame of a proton with spin in +z direction, what's the spatial dependence of the expectation of the electric charge operator $j^0(x)$, at some particular renormalization scale? Can this question be sufficiently answered by the currently available data from polarized proton scattering experiments?

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At the level of individual Proton interactions I reckon it is far more common to use the parton model, ie it is a collection of three quarks, $uud$, and associated gluons.

Also the 'spin' axis is a quantum physical term and is best not converted to classical terms.

nb. This answer was given to a previous, simpler vesion of the question.

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The fact that the parton model is commonly used does not make the question ill-defined. Parton distributions do not encode all information about the detailed shape (etc. charge distribution) of the proton. Parton model is applicable when the electron has high energy. But when the electron de-Broglie wavelength is comparable to the size of the proton, the outcome may be sensible to the proton's charge shape. –  felix Sep 5 '11 at 16:56
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Let me make my question more precise. In the rest frame of a proton with spin in +z direction, what's the spatial dependence of the expectation of the electric charge operator $j^0(x)$, at some particular renormalization scale? –  felix Sep 5 '11 at 17:02
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@felix: it wouldn't hurt to edit that sort of detail into your question. –  David Z Sep 6 '11 at 5:36
    
@David: thanks, I've done that. –  felix Sep 6 '11 at 6:56
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This is your call -- you haven't broke any rules. –  mbq Sep 6 '11 at 10:52
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