Extrapolation of Proton Electromagnetic Form Factor

Abstract

We use the assumed analytic properties of the proton electromagnetic form factors $G\left(t\right)\mathrm{}$ by performing a conformal transformation to a new variable $\eta$ such that the form factor is analytic inside the unit circle in the complex $\eta$ plane. We fit the data with power series in $\eta$ and extrapolate to the circle to find the spectral function. For both electric and magnetic form factors, we find spectral functions with a broad peak around 625 MeV, and a negative excursion above 1 BeV. We examine the validity of our extrapolation procedure by tests on several types of artificial data. Our procedure can reproduce a spectral function with a broad peak, but is not so successful in reproducing a narrow resonance, or a pair narrow resonances close together.