A High Precision Measurement of the Proton Charge Radius at JLab

Abstract

The elastic electron-proton ($e-p$) scattering and the spectroscopy of hydrogen atoms are the two traditional methods to determine the proton charge radius ($r_{p}$). In 2010, a new method using the muonic hydrogen ($\mu$H)\footnote{A muonic hydrogen has its orbiting electron replaced by a muon.} spectroscopy reported a $r_{p}$ result that was nearly ten times more precise but significantly smaller than the values from the compilation of all previous $r_{p}$ measurements, creating the ``proton charge radius puzzle".In order to investigate the puzzle, the PRad experiment (E12-11-106\footnote{Spokespersons: A. Gasparian (contact), H. Gao, M. Khandaker, D. Dutta}) was first proposed in 2011 and performed in 2016 in Hall B at the Thomas Jefferson National Accelerator Facility, with both 1.1 and 2.2 GeV electron beams. The experiment measured the $e-p$ elastic scattering cross sections in an unprecedented low values of momentum transfer squared region ($Q^2 = 2.1\times10^{-4} - 0.06~\rm{(GeV/c)}^2$), with a sub-percent precision.The PRad experiment utilized a calorimetric method that was magnetic-spectrometer-free. Its detector setup included a large acceptance and high resolution calorimeter (HyCal), and two large-area, high-spatial-resolution Gas Electron Multiplier (GEM) detectors. To have a better control over the systematic uncertainties, the absolute $e-p$ elastic scattering cross section was normalized to that of the well-known M$\o$ller scattering process, which was measured simultaneously during the experiment. For each beam energy, all data with different $Q^{2}$ were collected simultaneously with the same detector setup, therefore sharing a common normalization parameter. The windowless H$_2$ gas-flow target utilized in the experiment largely removed a typical background source, the target cell windows. The proton charge radius was determined as $r_{p} = 0.831 \pm 0.007_{\rm{stat.}} \pm 0.012_{\rm{syst.}}$~fm, which is smaller than the average $r_{p}$ from previous $e-p$ elastic scattering experiments, but in agreement with the $\mu$H spectroscopic results within the experimental uncertainties.