![]() To avoid model dependent bias in the radius extraction, the contributions of higher order terms should be kept minimal. At Q 2 ≈ 3 fm −2 the contributions of the Q 6 and Q 8 terms are not negligible and their omission from the fit causes a systematic shift in the determined radius. However, the radius obtained in this manner should not be trusted since the true shape of the G E p ( Q 2 ) may be more complex than a second order polynomial. In the first step the two parameters were determined by fitting Equation (2) to the data with Q 2 ≤ 3 fm −2, considering the entire region with the high density of experimental points. Since the data are normalized, the constant term of the model is simply 1. This model depends on two free parameters: the radius, r E, in front of the linear term, and the parameter a that determines the curvature of the function. In the first determination of the radius, existing data on proton charge form factor from five different measurements were considered, as noted in Table 1. In this paper we follow a different path and revisit the first data of Hand et al., and evaluate their result by using modern analysis techniques. ![]() These experiments have been accompanied by different reanalyses of the existing data, focusing on data of Bernauer et al. The observed discrepancy, colloquially known as “the proton radius puzzle” motivated several new experiments. This result was called into question when the extremely precise spectroscopic measurements on muonic hydrogen reported a significantly smaller value of 0.84087(39) fm. 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, ). , who determined the radius of 0.805(11) fm, the value used in the standard dipole parameterization of the form factor. The first determination of the radius was done with elastic electron scattering data by Hand et al. This optimal function, the Padé (0, 1) approximant, also gives a result which is consistent with the modern high precision proton radius extractions.Īnd can be determined by both hydrogen spectroscopy and elastic lepton scattering. We additionally made use of modern computing power to find a robust function for extracting the radius using this 1963 data's spacing and uncertainty. In trying to reproduce this classic result, we discovered that there was a sign error in the original analysis and that the authors should have found a value of 0.851(19) fm. In 1963, a proton radius of 0.805(11) fm was extracted from electron scattering data and this classic value has been used in the standard dipole parameterization of the form factor.
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