Abstract
We present a combined analysis of the electromagnetic form factors of the nucleon in the space- and timelike regions using dispersion theory. Our framework provides a consistent description of the experimental data over the full range of momentum transfer, in line with the strictures from analyticity and unitarity. The statistical uncertainties of the extracted form factors are estimated using the bootstrap method, while systematic errors are determined from variations of the spectral functions. We also perform a high-precision extraction of the nucleon radii and find good agreement with previous analyses of spacelike data alone. For the proton charge radius, we find r_{E}^{p}=0.840_{-0.002}^{+0.003} _{-0.002}^{+0.002} fm, where the first error is statistical and the second one is systematic. The Zemach radius and third moment are in agreement with Lamb shift measurements and hyperfine splittings. The combined dataset of space- and timelike data disfavors a zero crossing of μ_{p}G_{E}^{p}/G_{M}^{p} in the spacelike region. Finally, we discuss the status and perspectives of modulus and phase of the form factors in the timelike region in the context of future experiments, as well as the onset of perturbative QCD.
Highlights
We present a combined analysis of the electromagnetic form factors of the nucleon in the space- and timelike regions using dispersion theory
They provide a window on the strong interaction dynamics in the nucleon over a large range of momentum transfers
They are an important ingredient in the description of a wide range of observables ranging from the Lamb shift in atomic physics [6,7,8,9] over the strangeness content of the nucleon [10,11] to the EM structure and reactions of atomic nuclei [12,13,14]
Summary
Associated with each intermediate state is a branch cut starting at the corresponding threshold in t and running to infinity This analytic structure can be exploited to reconstruct the full form factor from its imaginary part given by Eq (2). The longest-range and, at low momentum transfer, most important continuum contribution to the spectral function ImFðtÞ comes from the 2π intermediate state, which contributes to the isovector form factors [49]. The remaining contributions to the spectral function above t ≈ 1 GeV2 can be parametrized by effective vector meson poles that are fitted to the form factor and cross section data. Since the analytical continuation from the space- to the timelike region is, strictly speaking, an illposed problem, the general strategy is to include as few effective poles as possible to describe the data in order to improve the stability of the fit [57]. Data type σðE; θÞ, PRad σðE; θÞ, MAMI μpGpE=GpM, JLab GnE, world GnM, world jGpeff j, world jGneff j, world jGE=GMj, BABAR dσ=dΩ, BESIII
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