Session DB: Determination of the Proton Radius: Recent Results

Applying Occam's Razor To The Proton Radius Puzzle

Over the past five decades, ever more complex mathematical functions have been used to extract the radius of the proton from electron scattering data. For example, in 1963 the proton radius was extracted with linear and quadratic fits of low Q$^2$ data ( $<$ 3~fm$^{-2}$ ) and by 2014 a non-linear regression of two tenth order power series functions with thirty-one normalization parameters and data out to 25~fm$^{-2}$ was used. But for electron scattering, the radius of the proton is determined by extracting the slope of the charge form factor at a Q$^2$ of zero. By using higher precision data than was available in 1963 and focusing on the low Q$^2$ data from 1974 to today, we find extrapolating functions consistently produce a proton radius of around 0.84~fm. A result that is in agreement with modern Lamb shift measurements.   

A coherent analysis of elastic electron-proton scattering data

The extraction of form factors and radii from scattering data is a treacherous business, and it is easy to bias the result with the choice of an unsuitable fit function. In the first part of the talk, I will present our analysis of the Mainz and world data sets, and the checks we have made to ensure that the results are accurate and unbiased. Recently, several authors have reanalyzed the Mainz and world data sets on electron-proton scattering, with the aim to extract the proton charge radius. The results fall into two groups: radii around 0.88 fm and around 0.84 fm, respectively. We find that the latter group typically is affected by various problems, discussed in the second part of the talk.   

Measurements of atomic splittings in atomic hydrogen and the proton charge radius

The proton charge radius can be determined from precise measurements of atomic hydrogen spectroscopy. A review of the relevant measurements will be given, including an update on our measurement of the n=2 Lamb shift. The values obtained from hydrogen will be compared to those obtained from muonic hydrogen and from electron-proton elastic scattering measurements.