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.

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We have measured the beam-normal single-spin asymmetry An in the elastic scattering of 1-3 GeV transversely polarized electrons from 1 H and for the first time from 4 He, 12 C, and 208 Pb. For 1 H, 4 He and 12 C, the measurements are in agreement with calculations that relate An to the imaginary part of the two-photon exchange amplitude including inelastic intermediate states. Surprisingly, the 208 Pb result is significantly smaller than the corresponding prediction using the same formalism. These results suggest that a systematic set of new An measurements might emerge as a new and sensitive probe of the structure of heavy nuclei.

Background: Extracting the proton charge radius from electron scattering data, requires determining the slope of the charge form factor at Q 2 of zero. As experimental data cannot reach that limit, numerous methods for making the extraction have been proposed.Purpose: In this study, we seek to find functional forms that will allow a robust extraction of the proton radius from a wide variety of functional forms. The primary motivation of this study is to have confidence in the extraction of upcoming low Q 2 experimental data. Method:We create a general framework for studying various form-factor functions along with various fitting functions. The input form factors are used to generate pseudo-data with fluctuations mimicking the binning and random uncertainty of a set of real data. All combinations of input functions and fit functions can then be tested repeatedly against regenerated pseudo-data. Since the input radius is known, this allows us to find fitting functions that are robust for proton radius extractions in an objective fashion.Results: For the range and uncertainty of the PRad data, we find that a two-parameter rational function, a two-parameter continued fraction and the second order polynomial expansion of z can extract the input radius regardless of the input charge form factor function that is used. Conclusions:We have created a framework to determine which functional forms allow for a robust extraction of the radius from pseudo-data generated from a wide variety of trial functions. By taking into account both bias and variance, the optimal functions for extracting the proton radius can be determined.