QED confronts the radius of the proton

Abstract

Recent results on muonic hydrogen [1] and the ones compiled by CODATA on ordinary hydrogen and $ep$-scattering [2] are $5\sigma$ away from each other. Two reasons justify a further look at this subject: 1) One of the approximations used in [1] is not valid for muonic hydrogen. This amounts to a shift of the proton's radius by $\sim 3$ of the standard deviations of [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 [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 $3.92\times 10^{-12}$. In this sense, this quantity is not empirically known. Its value would regulate the level of "tension" between muonic- and ordinary-hydrogen results, currently {\it at most} $\sim 4\sigma$. There is no tension between the results of [1] and the proton radius determined with help of the analyticity of its form factors.

Extended for publication in Physics Letters

References in corpus (4)

• Dispersion analysis of the nucleon form factors including meson continua
• Two-Loop Bethe Logarithms
• Chiral extrapolation of octet-baryon charge radii
• QED is not endangered by the proton's size

Cited by in corpus (20)

• The Proton Radius Puzzle
• Theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen
• Muonic hydrogen and MeV forces
• The RMS Charge Radius of the Proton and Zemach Moments
• New Parity-Violating Muonic Forces
• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Proton size anomaly
• Model independent extraction of the proton magnetic radius from electron scattering
• Model independent analysis of proton structure for hydrogenic bound states
• Non-perturbative evaluation of some QED contributions to the muonic hydrogen $\mathbf{n}=2$ Lamb shift and hyperfine structure
• Proton root-mean-square radii and electron scattering
• XUV frequency comb metrology on the ground state of helium
• Lamb shift in muonic deuterium atom
• Hyperfine structure of S-states in muonic deuterium
• Radiative nonrecoil nuclear finite size corrections of order $\alpha (Z\alpha {)}^5$ to the hyperfine splitting of S-states in muonic hydrogen
• Lamb shift in muonic ions of lithium, beryllium and boron
• Non-Perturbative Relativistic Calculation of the Muonic Hydrogen Spectrum
• Hyperfine structure of P-states in muonic deuterium
• Radiative and chiral corrections to elastic lepton-proton scattering in chiral perturbation theory
• Reduced Theoretical Error for QED Tests with 4He+ Spectroscopy