Abstract
The proton charge and magnetization density distributions can be related to the well known Sachs electromagnetic form factors G E,M (q 2) through Fourier transforms, only in the Breit frame. The Breit frame however moves with relativistic velocities in the Lab and a Lorentz boost must be applied before extracting the static properties of the proton from the corresponding densities. Apart from this, the Fourier transform relating the densities and form factors is inherently a non-relativistic expression. We show that the relativistic corrections to it can be obtained by extending the standard Breit equation to higher orders in its 1/c 2 expansion. We find that the inclusion of the above corrections reduces the size of the proton as determined from electron proton scattering data by about 4%.
Highlights
JHEP09(2015)215 surprising finding that the extracted value of rp = 0.84184(67) fm was much smaller than the world average CODATA value of 0.8768(69) fm [24, 25]
In an attempt to resolve the discrepancy between the proton radius from muonic hydrogen spectroscopy and electron proton scattering data, we re-examine the connection of the electromagnetic form factors to the nucleon properties
Instead of emphasizing the exact values, we conlcude this section by mentioning that the relativistic corrections and the Lorentz boost taken together cause a reduction of about 4% in the radius of the proton calculated from electron proton scattering
Summary
The relativistic corrections to the non-relativistic ρC(r) are obtained by extending the standard Breit equation [16, 17] (which involves an expansion of the amplitude to order 1/c2) [5,6,7, 31, 32] to higher orders. The proton electric potential Vp(r) in this equation is used to find the density ρC(r) via the Poisson equation, ∇2Vp = −4πρC. The hyperfine interaction terms in the Breit equation are shown to be related to the magnetization density ρM (r). We shall see that an interesting outcome of the calculation is that the charge form factor ρC(q2) appearing in the Fourier transform, depends on the magnetic form factor GM (q2) and ρM (q2) appearing in the Fourier transform of the magnetization density, ρM (r), depends on GE(q2)
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