# Neutron electric charge density

1. Feb 20, 2008

### humanino

I have not found a discussion open on this, and I would like to know if anybody has an opinion.
My questions are triggered by the 0802.2563 arXiv paper (Meson Clouds and Nucleon Electromagnetic Form Factors by G. Miller).

It has long been believed that the neutron electric charge density is positive near the core and negative at the periphery (integrating to zero). Naively, the neutron is likely to fluctuate in a proton and negative pion, with the light pion spreading over a large region. One-gluon exchange calculations performed by several "experts" confirm this. See for instance the references given in 0802.2563

Usually it is taught in kindergarden that the Sachs Form Factors (which parameterize the elastic electron-nucleon cross section) can be interpreted as the Fourier transforms of the electric charge and magnetic current densities. As compared to the Dirac and Pauli Form Factors, this parameterization has no cross term.

This interpretation of the Sachs FFs is spoiled by relativistic effects, since one cannot really probe a nucleon with a decent wavelength and not kick it with a large momentum at the same time. A quantitative analysis (Phys. Rev. D 69, 074014 (2004) or eq. 2.22 here) indicates that one needs
$$\frac{1}{R_{N}} \ll |\vec{\Delta}| \ll |\vec{p}| \ll M_{N}$$
where $$p$$ is the average momentum of the nucleon and $$\Delta$$ is the momentum transfer. The window is very narrow, since $$R_{N}M_{N}\sim 4.1$$.

However, a new interpretation has been proposed by G. Miller in Phys. Rev. Lett. 99, 112001 (2007) (just to let you know that the proceeding 0802.2563 is not the only one, there is a published paper in a respectable journal). It appears that one should really Fourier transform the Dirac FF to get the charge density. If one does so, one gets a negative charge at the center of the neutron (the previous features, in particular the negative meson cloud at long distance, is still present).

At the very least, the electric charge density so obtained is the one in the transverse plane for a nucleon on the light-cone. In fact, this "technical detail" seems crucial to me. Soper had realized long ago that there is a galilean subgroup of transverse boosts in the Poincare group. This had recently been braught back to life by Burkardt and his work on distribution of partons in the transverse plane.

This can be understood alternatively in terms of isospin symmetry and quarks. See Fig.4 in 0802.2563 if you are interested.

Well, I guess I forgot everything I used to know
I think this is really new and important.
I would appreciate any comment.

Last edited: Feb 20, 2008