Luxmi Machahari | Searcharxiv

arXiv2020

Analytical models of the Proton Structure Function and the gluon distribution at small x beyond leading order

We incorporate the next-to-leading order (NLO) and the next-to-next-to-leading order (NNLO) effects in the models of the Singlet Structure function F_2^S(x,t) and the gluon distribution G(x,t) using DGLAP equations approximated at small x. Analytical solutions both at the next-to leading order (NLO) as well as the next-to-next-to leading order (NNLO) are obtained. We then make comparisons with exact results.

hep-ph↗

arXiv2016

A study of structure functions with the DGLAP: equations at small $x$ with $O(x)$ and $O(x ^2 )$

We obtain a pair of second order differential equations in two variables $x$ and $t$ from the coupled DGLAP QCD evolution equations at small $x$ using the standard Taylor series expansion method.To that end we keep terms upto $O(x^2 )$.We use the standard assumption about the relationship between the singlet Structure Function and the gluon distributions available in current literature. We solve the taylor approximated $O(x)$ DGLAP equations by Lagrange's auxiliary method and $O(x^2)$ equation by Method of Separation of Variables and then show that the two solutions obtained in each for $O(x)$ and $O(x^2)$ are not identical in general.Analysis of the results obtained are done in the range of the recent HERA data.

hep-ph↗