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Transverse Charge Distribution of Hadrons

This work is done by the Nuclear Physics Group at the CUA, together with Dr. Gerald A. Miller, from the University of Washington.

According to Siddharth Venkat, 2010, having the form factor F(Q^2) of a particle it is possible to simplify the calculation of its two-dimensional transverse density using the finite radius approximation.

In this work we are going to calculate the transverse charge distribution of Pions. As a first step for this calculation, we are reproducing the Proton charge distribution from Siddharth Venkat, 2010.

Proton Transverse Charge Distribution

This section is a reproduction of the calculation done in Siddharth Venkat, 2010, using experimental data from ... (insert references here!)

In the case of protons, the measured form factors are G_e and G_m. They are linear combinations of F1 and F2, according to the following equations:

(insert equations)

The experimental data and the fit given by [Siddharth Venkat, 2010] for G_e and G_m are shown in the following figures:

Proton form factor G_e. Experimental data from XX and fit from [Siddharth Venkat, 2010].

Proton form factor G_m. Experimental data from XX and fit from [Siddharth Venkat, 2010].

These G_e and G_m form factors can be re-written in the F_1 and F_2 form factors. The results are shown in the following figures:

Proton form factor F_1(Q^2).

Proton form factor F_2(Q^2).

As the charge distribution are Fourier transforms of form factors, one can extract the charge distribution by performing this calculation. The first step is to calculate the mean radius of the proton. It is done by fitting the form factors in the limit of low Q^2.

Mean radius R_1 of the proton, related to the form factor F_1.

Mean radius R_2 of the proton, related to the form factor F_2.