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?