Properties of the Sachs electric form factor of the proton on the basis of recent e − p scattering experiments and hydrogen spectroscopy

Abstract

Recently published data on the Sachs electric form factor by the PRad collaboration (Nature 575, 147-151) are analyzed to investigate their consistency with the known proton charge radius from muonic and electronic hydrogen spectroscopy, as well as theoretical predictions from dispersively improved chiral perturbation theory. It is shown that the latter is fully consistent with the data, and pointers are given how future e − p scattering experiments can lead to an improvement of our knowledge of the form factor in the low-momentum-transfer regime. * marko@yorku.ca arXiv:1912.01735v4 [nucl-ex] 1 Feb 2020 R E = 0.879(8) fm. The radius R E enters the spectroscopic analysis via the slope of the Sachs electric form factor at zero momentum transfer squared Q 2 . The fact that hydrogen spectroscopy and e − p scattering are determining the same quantity is documented well in the literature [5].Since then, numerous efforts were undertaken to resolve the puzzle: (i) measurements on muonic deuterium [6] combined with the isotope shift, (ii) a fluorescence-based determination of the regular hydrogen 2S − 4P fine structure intervals [7], and (iii) a high-accuracy measurement of the Lamb shift in regular hydrogen [8] all pointed to a confirmation of the muonic hydrogen result; on the other hand (iv) a high-precision re-measurement of the 1S − 3S interval by the Paris group [9] continued to support the original higher value for the charge radius; this latter work is being contested by current fluorescence-detection work in Garching, which is achieving substantially higher precision.In more recent e − p scattering experiments both the Mainz group through a different method, based on intermediate-state radiation (ISR) [10] found consistency with the muonic charge radius (albeit with insufficient accuracy to make a strong case, so far), as did the PRad collaboration [11] which employed a gas jet target and measured projectile deflections directly.The situation still has the attention of both the spectroscopy and scattering communities, but the originally spread ideas that there could be new physics, i.e., that muons and electrons might behave differently have been damped by these developments.The significance of resolving the puzzle is not just academic, i.e., eventually, lattice gauge calculations within quantum chromodynamics will be able to compute at least certain aspects of the electric and magnetic form factors, and it will be good to have a solid understanding of the charge and current distributions of the proton based on experimental data. In addition, the determination of the charge radius leads to a significant change in the Rydberg constant

Precise determination of the proton magnetic radius from electron scattering data

“…This happens because the DIχ EFT model naturally describes the Q 2 dependence of the low-Q 2 data, with the same value of r p E as favored by the higher-Q 2 data [20]; this was also observed in the analysis of Ref. [23]. Note that the low-Q 2 data are sensitive mostly to r p E , and that our present extraction of r p M requires us to include data up to Q 2 ≈ 0.5 GeV 2 .…”

“…Apparent discrepancies between the different extraction methods (the "proton radius puzzle") have engendered intense experimental and theoretical efforts, including dedicated new elastic scattering experiments at low Q 2 with electron and muon beams [11,12]. Most recent experiments and reanalyses have converged around r p E = 0.84 fm [11,[13][14][15][16][17][18][19][20][21][22][23][24], while some have obtained larger values [25][26][27][28]; the CODATA Task Group and the Particle Data Group have now adopted 0.84 fm as the recommended value [29,30]. The proton magnetic radius can only be extracted from elastic FF measurements (a method using atomic measurements was proposed in Ref.…”

The quest for the proton charge radius

“…These two quantities are in very strong correlation, with a correlation coefficient 0.9891. For the proton rms charge radius they obtained 20 r p = 0.8335 (95) This work is being contested by fluorescence-detection work in Garching, which is achieving higher precision 52 .…”

The proton charge radius

“…Horbatsch (Horbatsch, 2020) analyzed the PRad data on the proton G E following a proposal by Hagelstein and Pascalutsa (Hagelstein and Pascalutsa, 2019) by taking the logarithm to yield a Q 2 dependent radius function. This analysis shows that the PRad data is in agreement with theoretical predictions from dispersively improved chiral perturbation theory.…”