QED confronts the radius of the proton

摘要

Recent results on muonic hydrogen (Pohl et al., 2010) 1 and the ones compiled by CODATA on ordinary hydrogen and ep-scattering (Mohr et al., 2008) 2 are 5 σ away from each other. Two reasons justify a further look at this subject: (1) One of the approximations used in Pohl et al. (2010) 1 is not valid for muonic hydrogen. This amounts to a shift of the proton's radius by ～3 of the standard deviations of Pohl et al. (2010) 1, in the "right" direction of data-reconciliation. In field-theory terms, the error is a mismatch of renormalization scales. Once corrected, the proton radius "runs", much as the QCD coupling "constant" does. (2) The result of Pohl et al. (2010) 1 requires a choice of the "third Zemach moment". Its published independent determination is based on an analysis with a p-value - the probability of obtaining data with equal or lesser agreement with the adopted (fit form-factor) hypothesis - of 3.92×10-12. In this sense, this quantity is not empirically known. Its value would regulate the level of "tension" between muonic- and ordinary-hydrogen results, currently at most ～4σ. There is no tension between the results of Pohl et al. (2010) 1 and the proton radius determined with help of the analyticity of its form-factors.