Method for robust extraction of proton charge radius from electron-proton-scattering experiments*

A lot of efforts have been devoted to the measurements of the radius of the proton charge distribution ($R$), but results from different experiments and/or analyses have sizable differences. In high-precision muonic hydrogen Lamb shift experiments, $R$ was measured to be $0.8409 \pm 0.0004$ fm, while typical global data analyses of the electron-proton ($ep$) scattering experiments yielded $R = 0.879 \pm 0.009$ fm. This difference has been known as the proton radius puzzle. Some recent global $ep$-scattering-data analyses found $R \approx 0.84$ fm, but the fitting methods used by them were criticized by others in the literature. We formulated a robust fitting method to find the ``real" $R$ in upcoming $ep$-scattering experiments. Comprehensive tests have been carried out using the binning and statistical uncertainties of the PRad experiment (E12-11-106\footnote{Spokespersons: A. Gasparian (contact), H. Gao, M. Khandaker, D. Dutta}). In this talk, we will discuss the details of this method and present the test results.