Proton Electro-Magnetic Form-Factors in the Instanton Liquid Model

Abstract

We report the first non-perturbative calculation of proton electro-magnetic form-factors in the Random Instanton Liquid Model (RILM) and in the Interacting Instanton Liquid Model (IILM). By calculating the ratio of appropriate three-point to two-point functions, we divide out the coupling constants and compare our results directly to some integral of the form-factors. Using various parameterizations of the electric form-factor $G_E(Q^2)$ at large $Q^2>3.5 GeV^2$, where it is not yet measured, we compare those with expected theoretical dependence. We find from this comparison that some distributions of charge are clearly excluded (e.g. the same as of the magnetic moment, $μG_E/G_M=1$, as well as the opposite scenario in which $μG_E/G_M$ rapidly approach zero), restricting possible behavior of the form-factor to rather narrow band. Furthermore, we found that our calculation of the nucleon form-factors is dominated by a configuration in which two out of three quarks interact with a $single$-instanton, in spite of the fact that the evaluated three-point function has rather large distances ($\sim 1.2 fm$) between points. We also estimate the size of the scalar di-quark and found it to be very small, comparable to the typical instanton size.