Solution of non-singlet DGLAP evolution equation in leading order and next-to-leading order at small-x by method of characteristics

TL;DR

This paper solves the non-singlet DGLAP evolution equations at small-x in LO and NLO using the method of characteristics, providing solutions that are compared with experimental data from Fermilab and NMC.

Contribution

It introduces a Taylor series expansion combined with the method of characteristics to solve DGLAP equations at small-x in LO and NLO, offering a new analytical approach.

Findings

Solutions agree with Fermilab E665 data

Solutions agree with NMC data

Method provides a new analytical technique for DGLAP equations

Abstract

The non-singlet structure functions have been obtained by solving Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations in leading order (LO) and next-to-leading order (NLO) at the small-x limit. Here a Taylor series expansion has been used and then the method of characteristics has been applied to solve the evolution equations. Results are comopared with the Fermilab experiment E665 data and New Muon Collaboration (NMC) data.