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In the press release of the recent measurement of the proton structure, they barely mention various theoretical explanations for the effect. What is the most likely (not assuming now that the experiment is wrong)? What exactly should be modified in QED or in other theories? (Some pointer for the current explanations would also be appreciated)

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Given that is is known that the proton in a nuclear context is not the same as free proton (and that we can not fully describe the difference in closed form) I don't find it surprising that the proton in a muon-atomic context differs from that in a electron-atomic context. Albeit I would expect the difference to be small. These spectroscopic measurements are enormously sensitive if the the theory is up to it). I wouldn't look for the difference in QED, but in QCD. Alas we don't have a fully description of any proton in QCD, so ... –  dmckee Jun 10 '13 at 15:12
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