Analytic Derivation of the Quark Distribution Functions Near x=1 by Statistical Methods

Abstract

In this paper, we made a statistical approach on the thermodynamic structure of the nucleon and its quark distributions. We assume that the nucleon is a thermodynamic system of quarks and gluons. After we derived the quark density of states from the Dirac Equation, we calculated each quark's chemical potential, associating it with the quark's spin distribution. By using the sum rule of the longitudinal momentum, we obtain a function showing the relation between the temperature, radius and mass of the nucleon. The nucleon's radius is determined by the total energy minimal principle, and thus the temperature is also known. Finally, we deduced the quark distribution functions near x=1, and the results are in agreement with the experimental data.