Abstract
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 5σ 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.
Highlights
The results of a measurement by Pohl et al [1] of the Lamb shift in muonic hydrogen and those compiled by CODATA on ordinary hydrogen and ep-scattering [2] are ∼ 5 σ away from each other
The authors of [1] conclude “Our result implies that either the Rydberg constant has to be shifted by 2110 kHz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient.”
I discuss why the second option is part of the resolution of the apparent conundrum, but not all of it. It is intrepid [3] to use a model of the proton –in [1], a dipole form-factor– to challenge very well established physics –such as QED [1, 4]. This is not the only bone of contention: One of the approximations used in the theory of ordinary or muonic hydrogen involves the lepton’s wave function at the origin
Summary
The results of a measurement by Pohl et al [1] of the Lamb shift in muonic hydrogen and those compiled by CODATA on ordinary hydrogen and ep-scattering [2] are ∼ 5 σ away from each other. I discuss why the second option is part of the resolution of the apparent conundrum, but not all of it It is intrepid [3] to use a model of the proton –in [1], a dipole form-factor– to challenge very well established physics –such as QED [1, 4]. The modification results in a ∼ 3 σ(μH) shift of the extracted central value of rp, in the direction of reducing the “tension” between experimental results This correction depends on the model of the proton’s charge distribution, but the model-dependence is a small correction to a moderate correction.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
