Understanding the systematic differences in extractions of the proton electric form factors at low
Jingyi Zhou (Department of Physics, Duke University, Durham, North Carolina 27708, USA, Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA); Vladimir Khachatryan (Department of Physics, Duke University, Durham, North Carolina 27708, USA, Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA); Haiyan Gao (Department of Physics, Duke University, Durham, North Carolina 27708, USA, Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA); Simon Gorbaty (Department of Physics, Duke University, Durham, North Carolina 27708, USA, Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA); Douglas W. Higinbotham (Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA)
Systematic differences exist between values of the proton's electric form factors in the low- region extracted by different experimental and theoretical groups, though they are all making use of basically the same electron-proton scattering data. To try to understand the source of these differences, we make use of the analytically well-behaved rational () function, a predictive function that can be reasonably used for extrapolations at . First, we test how well this deceptively simple two-parameter function describes the extremely complex and state-of-the-art dispersively improved chiral effective field theory calculations. Second, we carry out a complete re-analysis of the 34 sets of electron-proton elastic scattering cross-section data of the Mainz A1 Collaboration with its unconstrained 31 normalization parameters up to . We find that subtle shifts in the normalization parameters can result in relatively large changes in the extracted physical qualities. In conclusion, we show that by simply using a well-behaved analytic function, the apparent discrepancy between recent form-factor extractions can be resolved.