Comparative analysis of analytical solutions for $F_2^P$ at small $x$ in DGLAP approach

TL;DR

This paper compares analytical solutions for the proton structure function $F_2^P$ at small $x$ using DGLAP equations, employing Lagrange's and Method of Characteristics, with data favoring Lagrange's approach.

Contribution

It introduces analytical solutions to coupled DGLAP equations using two mathematical methods and compares their effectiveness against experimental data.

Findings

Lagrange's method provides solutions more compatible with experimental data.

Analytical solutions are successfully derived for the proton structure function.

Comparison highlights the effectiveness of different mathematical approaches in QCD analysis.

Abstract

Coupled DGLAP equations involving singlet quark and gluon distributions are explored by a Taylor expansion as two first order partial differential equations in two variables. The system of equations are then solved by the Lagrange's method and Method of Characteristics. We obtain the proton structure function by combining the corresponding non-singlet and singlet structure functions by both the methods. Analytical solutions for proton structure function thus obtained are compared with the data available and their compatibility is checked. Data favors the analytical solution by Lagrange's method.