Abstract
In the quantum statistical parton distributions approach proposed more than one decade ago to describe the parton structure, new properties are now understood, in particular, the relation between quarks and antiquarks which leads to very specific properties. The simultaneous treatment of unpolarized and polarized Parton Distribution Functions (PDFs) allows a determination of thermodynamical potentials (the master parameters of the model) which drive their behavior and as a consequence those of the structure functions. The existence of a possible relation between the gluon and a $q~\bar q$ pair leads to define a toy model for the unpolarized and polarized gluon. In view of forthcoming experimental results in the large $x$ region specific predictions made by the model are presented.
Highlights
The main objective is to build a quark structure where constitutive elements can be understood through their parameters, which are associated with the quark properties
The statistical approach is characterized by thermodynamical potentials whose values are the master parameters; they drive the shape of the parton distribution functions (PDFs) but are found to control some specific properties of the structure functions
To conclude this part devoted to the statistical model, the present formulas used as a toy parametrization of unpolarized and polarized gluons give an equivalent description of the original model, and they represent a new test for the antiquark PDFs since the quark PDFs are well established
Summary
The main objective is to build a quark structure where constitutive elements can be understood through their parameters, which are associated with the quark properties. The statistical approach is characterized by thermodynamical potentials whose values are the master parameters; they drive the shape of the parton distribution functions (PDFs) but are found to control some specific properties of the structure functions. In order to introduce the maximum constraints, we decided to work from the beginning with helicity components, which are the building blocks of both the polarized and unpolarized PDFs; a unique situation in the domain.
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