A fifth order perturbative solution to the Gribov - Lipatov equation

TL;DR

This paper derives a fifth order perturbative solution for the Gribov-Lipatov equation in QED, improving accuracy in electron structure function calculations within the leading logarithmic approximation.

Contribution

It introduces a fifth order exact correction method using a recurrence formula and compares it with existing third order solutions, enhancing precision in QED structure functions.

Findings

Fifth order corrections improve accuracy over third order solutions.

Numerical parametrization achieves better than 5×10^-6 accuracy.

The method extends the perturbative series for non-singlet electron structure functions.

Abstract

Fifth order exact corrections to the non-singlet electron structure function in QED are the leading logarithmic approximation using the ad hoc exponentiation prescription proposed by Jadach and Ward and a recurence formula for the elements of the Jadach-Ward series. A comparison with existing third order solutions is also presented. The three next elements of the Jadac Ward series were calculated numerically and parametrized with an accuracy better than 5x10^-6 in the range of x between 0.01 and 1.