New properties of the parton statistical model

The Quantum Chromo Dynamical theory provides the most successfull framework to calculate the interaction between quarks the ultimate constituants of matter. In this theory the quarks are described by probability distributions which depnd on the fraction momentum they carry, but their true expression is unknown, so one is led to make approximations with standard polynomials. In front of such situation, we have proposed a more physical approach through Fermi or Bose Einstein distributions which depend on the quarks spin helicity a unique feature. These distributions involve a certain number of free parameters which are determined from experimental data. We prove that these parameters correspond in fact to an optimal solution for the distributions; and also that the calculation of the entropy of a proton state shares the same optimal property. Quarks are linked together by the gluons field, a detailed study of the polarized gluon lead us to introduce besides the Bose distribution a sigmoïd or activation function giving a new picture analogous to a neural structure. We have proven that this neural approach can be extended to quarks.