Determination of the moments of the proton charge density: is there a proton radius puzzle?

The charge radius of the proton can be determined using two different kinds of experiments: the spectroscopy technique, measuring the hyperfine structure of hydrogen atoms, and the scattering technique, deducing the radius from elastic lepton scattering off a proton target. These two methods lead to quite different results, a discrepancy known as the "proton radius puzzle ". To shed light on this problem, we have proposed a novel method for the determination of spatial moments from densities expressed in the momentum space. This method provides a direct access not only to the second order moment, directly related to the proton radius, but to all moments of any real order larger than -3. The method is applied to the global analysis of proton electric form factor experimental data from Rosenbluth separation and low-$Q^2$ experiments, paying specific attention to the evaluation of the systematic errors. Within this analysis, the integer order moments of the proton charge density are evaluated, the moment of second order leading to a new determination of the proton charge radius.