Evaluation of the strength of electron-proton scattering data for determining the proton charge radius

Abstract

Precisely measured electron-proton elastic scattering cross sections [Phys. Rev. Lett. 105, 242002 (2010)] are reanalyzed to evaluate their strength for determining the rms charge radius (RE) of the proton. More than half of the cross sections at lowest Q 2 are fit using two single-parameter formfactor models, with the first based on a dipole parametrization, and the second on a linear fit to a conformal-mapping variable. These low-Q 2 fits extrapolate the slope of the form factor to Q 2 =0 and determine RE values of approximately 0.84 and 0.89 fm, respectively. Fits spanning all Q 2 , in which the single constants are replaced with cubic splines at larger Q 2 , lead to similar results for RE. We conclude that the scattering data is consistent with RE ranging from at least 0.84 to 0.89 fm, and therefore cannot resolve the discrepancy between determinations of RE made using muonic and electronic hydrogen-atom spectroscopy. PACS numbers: \pacs{06.20. Jr,13.40.Gp,14.20.Dh,25.30.Bf} Recent measurements of the n=2 energy intervals of muonic hydrogen, when compared to precise QED theory for this exotic atom, lead to a determination [1,2] of the rms charge radius of the proton (R E ) of 0.84087(39) fm. This value disagrees by 4.5 standard deviations with a value of 0.8758(77) fm obtained from a similar comparison [3] between QED theory and several precision measurements in the ordinary hydrogen atom. A third determination of R E can be obtained from precise measurements of the the cross sections for elastic scattering between electrons and protons. The most precise electronproton scattering experiment is the recent measurement [4] of the MAMI collaboration, and their analysis [5] leads to R E = 0.879(8) fm, which disagrees with the muonic hydrogen value by 4.6 standard deviations.CODATA [3] uses a combination of the scattering and hydrogen values to obtain R E , and its value differs from the muonic hydrogen value by 7 standard deviations. This disagreement has now widely been referred to as the proton size puzzle [6]. Many papers have discussed this puzzle, including many that have proposed physics beyond the standard model [7].Because of the importance of the electron-proton scattering data to this puzzle, the data has been extensively scrutinized and discussed [5,[8][9][10][11][12][13][14][15][16][17][18][19][20]. The present work reanalyzes the scattering data and concludes that it is consistent with a much larger range of R E values than obtained by others. This range makes it consistent with both the hydrogen and muonic hydrogen determinations of R E , therefore removing one component of the proton radius puzzle.Our analysis uses two separate simple one-parameter form-factor models. Both of these simple models fit well to the low-Q 2 data, but the two give discrepant values for R E . Since neither model can be ruled out, the uncertainty in R E must, at minimum, be expanded to en- * hessels@yorku.ca compass both values. Generalizations of both models fit well to the entire MAMI data set, and give similarly dis...

Hydrogen molecular ions for improved determination of fundamental constants

“…Although many efforts have been undertaken in the last few years, no convincing solution of the "proton size puzzle" has been found so far (see [8] for a review). One of the possible explanations is that the error bars, both of hydrogen spectroscopy and scattering experiments [9] were underestimated. New scattering experiments are in preparation or underway, including electron-proton [10], electron-deuteron [11] and muon-proton scattering [12].…”

Proton radius from electron-proton scattering and chiral perturbation theory

“…[24], it was shown that values of R p ranging from 0.84 to 0.89 fm are possible from acceptable fits of the MAMI data, with the value of R p depending on the functional forms of G E and G M that are used for the extrapolation to Q 2 =0. In particular, the higher moments assumed by the different functional forms lead to the wide range of R p values.…”

“…The implication of that work [24] is that a precise value of R p cannot be obtained from electron-proton elastic scattering, unless precise lower-Q 2 data become available, or unless there are external constraints on the functional form of G E (Q 2 ) and G M (Q 2 ). The latter (external constraints on the functional forms -as obtained from chiral perturbation theory)…”

“…The determination of R p from electron-proton scattering data has been discussed extensively in the literature [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. The proton radius can be determined [24] from scattering data from…”

“…[24]. Before performing the fits, we remove the Feshbach two-photon-exchange correction and replace it with the more complete two-photon-exchange correction calculated following the prescription of Ref.…”