Estimating Quantum Statistical Parton Distribution Functions in proton by maximum entropy method

An attempt to extend simple Parton Distribution Functions based on the quantum statistical model to consider more active flavors is presented here. Considering partons as clusters, inspiring from the static picture of proton composed of three valence quarks, such a reasonable extension is surveyed to improve the results. Analytic expressions for the longitudinal Quantum Statistical Parton Distribution Functions are obtained by applying the maximum entropy principle beside theoretical proton sum rules. Furthermore, the main purpose of this study is to predict a minimum energy scale to probe the proton with a defined condition, theoretically. An interesting approach to determine the statistical variables exactly without fitting and fixing is employed and the consistency of computed distributions with the experimental observations gives a robust confirm of presented simple statistical model.