Realistic Transverse Images of the Proton Charge and Magnetic Densities

Abstract

We develop a technique, denoted as the finite radius approximation (FRA), that uses a two-dimensional version of the Shannon-Nyquist sampling theorem to determine transverse densities and their uncertainties from experimental quantities. Uncertainties arising from experimental uncertainties on the form factors and lack of measured data at high $Q^2$ are treated. A key feature of the FRA is that a form factor measured at a given value of $Q^2$ is related to a definite region in coordinate space. An exact relation between the FRA and the use of a Bessel series is derived. The proton Dirac form factor is well enough known such that the transverse charge density is very accurately known except for transverse separations $b$ less than about 0.1 fm. The Pauli form factor is well known to $Q^2$ of about 10 GeV${}^2$, and this allows a reasonable, but improvable, determination of the anomalous magnetic moment density.

11 pages, 9 figures

References in corpus (8)

• Nucleon Electromagnetic Form Factors
• Global analysis of proton elastic form factor data with two-photon exchange corrections
• Nucleon electromagnetic form factors
• Charged pion form factor between $Q^2$=0.60 and 2.45 GeV${}^2$. I. Measurements of the cross section for the ${}^1$H($e,e^{\prime }{\pi }^{+}$)$n$ reaction
• Scaling study of the pion electroproduction cross sections and the pion form factor
• Electromagnetic Form Factors and Charge Densities From Hadrons to Nuclei
• Quantifying the nucleon's pion cloud with transverse charge densities
• Proton Electromagnetic Form Factor Ratios at Low Q^2

Cited by in corpus (32)

• 50 Years of Quantum Chromodynamics
• Precision Measurement of the Weak Charge of the Proton
• Proton and neutron electromagnetic form factors and uncertainties
• The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability
• Generalized parton distributions and transverse densities in a light-front quark-diquark model for the nucleons
• Nucleon Form Factors - A Jefferson Lab Perspective
• Two-photon exchange correction to the hyperfine splitting in muonic hydrogen
• Two-photon exchange from intermediate state resonances in elastic electron-proton scattering
• Nucleon relativistic polarization and magnetization distributions
• PRad-II: A New Upgraded High Precision Measurement of the Proton Charge Radius
• The recoil correction to the proton-finite-size contribution to the Lamb shift in muonic hydrogen
• Model-independent determination of the magnetic radius of the proton from spectroscopy of ordinary and muonic hydrogen
• Deuteron transverse densities in holographic QCD
• Charge and longitudinal momentum distributions in transverse coordinate space
• Form factors and transverse charge and magnetization densities in the hard-wall AdS/QCD model
• A self-consistent value of the electric radius of the proton from the Lamb shift in muonic hydrogen
• Pion transverse charge density and the edge of hadrons
• Generalized parton distributions in the soft-wall model of AdS/QCD
• Charge and magnetization densities in transverse coordinate and impact parameter space
• Advanced extraction of the deuteron charge radius from electron-deuteron scattering data
• Transverse charge density and the radius of the proton
• Transverse Momentum and Transverse Momentum Distributions in the MIT Bag Model
• Exploring Baryon Resonances with Transition Generalized Parton Distributions: Status and Perspectives
• Transverse charge and current densities in the nucleon from dispersively improved chiral effective field theory
• Transverse densities and generalized parton distributions of $\rho$ meson in light front quark model
• Form factors of the nucleon by using the t dependence of parton distribution functions
• Two-dimensional charge distributions of the $\Delta$ baryon: Interpolation between the nonrelativistic and ultrarelativistic limit
• Systematic effects in the low-energy behavior of the current SAID solution for the pion-nucleon system
• Kaon transverse charge density from space- and timelike data
• Light-front dynamic analysis of the longitudinal charge density using the solvable scalar field model in (1+1) dimensions
• Cottingham formula for the electromagnetic self-energy contribution to M_p - M_n
• Comparison of results for the electromagnetic form factors of the proton at low $Q^2$