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

Luxmi Machahari; D. K. Choudhury; P. K. Sahariah

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arXiv · 1612.08576

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

Luxmi Machahari·D. K. Choudhury·P. K. Sahariah

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Abstract

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.

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Luxmi Machahari, D. K. Choudhury, P. K. Sahariah. 2016-12-27. A study of structure functions with the DGLAP: equations at small $x$ with $O(x)$ and $O(x ^2 )$. https://arxiv.org/abs/1612.08576

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