A small proton charge radius from an electron–proton scattering experiment

Abstract

Elastic electron-proton scattering (e−p) and the spectroscopy of hydrogen atoms are the two traditional methods used to determine the proton charge radius (r p). About a decade ago, a new method using muonic hydrogen (µH) atoms 1 found a significant discrepancy with the compilation of all previous results 2 , creating the "proton radius puzzle". Despite intensive worldwide experimental and theoretical efforts, the "puzzle" remains unresolved. In fact, a new discrepancy was reported between the two most recent spectroscopic measurements on ordinary hydrogen 3, 4. Here, we report on the PRad experiment, the first high-precision e − p experiment since the emergence of the "puzzle". For the first time, a magnetic-spectrometerfree method was employed along with a windowless hydrogen gas target, which overcame several limitations of previous e − p experiments and reached unprecedented small angles.

Reinterpretation of Classic Proton Charge Form Factor Measurements

“…2 shows that the radius depends almost linearly on a and reveals that the original value of r E can be reproduced if a, determined in the first step of our analysis, is used, but with the opposite (wrong) sign. To confirm this hypothesis, we again fitted model (2) to the data with Q 2 < 1.05 fm −2 , but this time kept the radius fixed at 0.805 (11) fm and adjusted only a. We obtained a = −0.00749(63) fm 4 , which strongly supports our assumption that a mistake was made in the original analysis.…”

“…The result of this work compared to other extractions of the proton charge radius. Full circles show findings of modern nuclear scattering experiments ( [11,[32][33][34]) together with the original result of Hand et al [2]. Full squares represent values obtained from the recent atomic hydrogen spectroscopy measurements ( [9,10,12]).…”

“…and can be determined by both hydrogen spectroscopy and elastic lepton scattering [1]. The first determination of the radius was done with elastic electron scattering data by Hand et al [2], who determined the radius of 0.805 (11) fm, the value used in the standard dipole parameterization of the form factor [3,4]. The original study was followed by several decades of dedicated nuclear scattering and spectroscopic experiments, which led to a recommended value for the proton charge radius of 0.8791(79) fm (CODATA 2010, [5]).…”

“…This result was called into question when the extremely precise spectroscopic measurements on muonic hydrogen [6,7] reported a significantly smaller value of 0.84087 (39) fm. The observed discrepancy, colloquially known as "the proton radius puzzle" [8] motivated several new experiments [9][10][11][12]. These experiments have been accompanied by different reanalyses of the existing data [13][14][15][16][17][18][19][20], focusing on data of Bernauer et al [21,22].…”

The proton radius: from a puzzle to precision

“…Lamb shift [17] 0.833 (10) 2019 el. Lamb shift [18] 0.831(7)(12) 2019 e − p scattering [19] a small radius in the range r p = 0.82 . .…”