Motion of quarks inside the neutron

[TheMan112]

Using electron-neutron scattering I'm trying to find out how the three quarks (udd) behave inside the neutron. S.Kopeky (Phys. Rev. 1995) found that for small Q² the equation for the neutrons rms-radius goes towards:

$$-6 \hbar \frac{dG_E ^n (Q^2)}{dQ^2} \right|_{Q^2=0} = -0.113 \pm 0.005 {fm}^2$$

I'm not sure how to draw conclusions from this. I imagine the charge density being the highest at the neutron boundary and lower towards the center, this leads me to conclude that the probablity for finding any of the quarks is equal and the highest at the boundary and lowest at the center. Since the charges are +2/3, -1/3, -1/3 respectively they should then all cancel each other out at the boundary making the neutron appear non-charged from the outside.

 

[BenTheMan]

I think you have to get this information from the Lattice---I think there's lots of non-perturbative goo that you have to deal with.

 

[humanino]

The assumptions leading to "the slope of the Sachs FF around zero is proprtional to the mean squared radius" are fairly strong. I can go into the details if you want, but basically you have a non-relativistic approximation relying on RM being large (with R the typical size and M the typical mass of the distribution you are probing). For the nucleon, RM~4.

In any case, those approaches are outdated by now. Generalized parton distributions contain the charge distributions in the transverse (spatial) plane as a function of the momentum fraction (xB). They can be (and are) calculated on the lattice. They can be (and are) measured, and modeled. The field is very active on all fronts I think.

edit
For all and more than you want on that
hep-ph/0504030