Measurement of the Generalized Polarizabilities of the Proton in Virtual Compton Scattering

We propose to conduct a measurement of the Virtual Compton Scattering reaction in Hall C that will allow the precise extraction of the two scalar Generalized Polarizabilities (GPs) of the proton in the region of $Q^2=0.05~(GeV/c)^2$ to $Q^2=0.50~(GeV/c)^2$. The Generalized Polarizabilities are fundamental properties of the proton, that characterize the system's response to an external electromagnetic (EM) field. They describe how easily the charge and magnetization distributions inside the system are distorted by the EM field, mapping out the resulting deformation of the densities in the proton. As such, they reveal unique information regarding the underlying system dynamics and provide a key for decoding the proton structure in terms of the theory of the strong interaction that binds its elementary quark and gluon constituents together. Recent measurements of the proton GPs have challenged the theoretical predictions, particularly in regard to the electric polarizability. The magnetic GP, on the other hand, can provide valuable insight to the competing paramagnetic and diamagnetic contributions in the proton, but it is poorly known within the region where the interplay of these processes is very dynamic and rapidly changing.The unique capabilities of Hall C, namely the high resolution of the spectrometers combined with the ability to place the spectrometers in small angles, will allow to pin down the dynamic signature of the GPs through high precision measurements combined with a fine mapping as a function of $Q^2$. The experimental setup utilizes standard Hall C equipment, as was previously employed in the VCS-I (E12-15-001) experiment, namely the HMS and SHMS spectrometers and a 10 cm liquid hydrogen target. A total of 59 days of unpolarized 75 $\mu A$ electron beam with energy of 1100 MeV (6 days) and 2200 MeV (53 days) is requested for this experiment.