Proton electromagnetic-form-factor ratios at low Q2

Area of Science:

• Nuclear Physics
• Particle Physics
• Quantum Chromodynamics

Background:

• The ratio R = μGE(Q2)/GM(Q2) describes proton electromagnetic form factors at low momentum transfer (Q2).
• Associated radii are not direct moments of charge or magnetization densities.
• Previous studies indicated a reduction of R as Q2 increases, suggesting differing spatial extents.

Purpose of the Study:

• To analyze the proton's form factors GE(Q2) and GM(Q2) at very small Q2.
• To investigate the spatial distribution of proton charge and magnetization densities.
• To establish a relationship between the measurable ratio R and moments of these densities.

Main Methods:

• Interpreting the form factor F2 as a 2D Fourier transform of magnetization density.
• Deriving a relationship between the measurable ratio R and moments of charge and magnetization densities.
• Analyzing the spatial extent of charge and magnetization densities based on derived relationships.

Main Results:

• The proton form factor F2 is shown to be the 2D Fourier transform of a magnetization density.
• A direct relationship between the ratio R and moments of true charge and magnetization densities was derived.
• The derived relationship indicates that proton magnetization density extends further than its charge density.

Conclusions:

• Proton magnetization density has a larger spatial extent than its charge density.
• This finding contrasts with expectations derived from the observed reduction of R as Q2 increases.
• The study provides a new interpretation of proton structure at low momentum transfer.