Abstract
Pohl et al. have reported a very precise measurement of the Lamb-shift in muonic hydrogen (Pohl et al., 2010) [1], from which they infer the radius characterizing the proton's charge distribution. The result is 5 standard deviations away from the one of the CODATA compilation of physical constants. This has been interpreted (Pohl et al., 2010) [1] as possibly requiring a 4.9 standard-deviation modification of the Rydberg constant, to a new value that would be precise to 3.3 parts in 1013, as well as putative evidence for physics beyond the standard model (Flowers, 2010) [2]. I demonstrate that these options are unsubstantiated.
Highlights
The dipole form factor is but a rough description of higher-energy data and is unacceptable on grounds of the analyticity requirements stemming from causality and the locality of fundamental interactions
The proton’s relativistic form factor, GE(q2), is expected, in the timelike domain q2 ≥ 0, to have a complex structure, with a first cut starting at q2 = 4 m2π and a plethora of branch cuts and complex resonant poles thereafter [4]
Even if we took the sixth root of this number to bring it closer to unity –as experimentalists do with r2 to halve the relative error– the result would, at the required great precision, still epitomize the model-dependence of the results
Summary
The conclusion is not that the experiments or the theory are wrong, but that the model (the customary dipole form factor) is inadequate at the level of precision demanded by the data. The experiments and QED are right, the dipole is wrong. The dipole form factor is but a rough description of higher-energy data and is unacceptable on grounds of the analyticity requirements stemming from causality and the locality of fundamental interactions. Any simple one-parameter description of the proton’s non-relativistic Sacks form factor, GE(−q2) in terms of only one mass parameter is inaccurate: the proton is not so simple. The proton’s relativistic form factor, GE(q2), is expected, in the timelike domain q2 ≥ 0, to have a complex structure, with a first cut starting at q2 = 4 m2π and a plethora of branch cuts and complex resonant poles thereafter [4]. Ρp(r) is expected to have a “core” and a “pion cloud” [5], corresponding to a minimum of two length parameters
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