An Analysis of the Proton Structure Function and the Gluon Distributions at Small x

Abstract

Recently, we reported an analysis of Proton structure function at small x based on Taylor approximated DGLAP equations assuming a plausible relationship between the singlet and the gluon distributions. In this paper, we report a generalised version of the previous work. A corresponding study of the suggested gluon distribution is also made. The present generalised version of the model for the structure function results in a wider x range of phenomenological validity than the earlier one. A comparison of both the models of the proton structure function and the gluon distribution is made with exact result as well as with the Froissart saturated models of Block, Durand and Mckay.

Analytical models of the proton structure function and the gluon distribution at small x beyond leading order

“…Specifically at double asymptotic limit (ultra small x and ultra large Q 2 ) the corresponding gluon and the singlet distribution have different x dependence in general. [2,36,37]. Thus the present assumption appears to be approximately true at limited x and Q 2 as has been observed in the present work.…”

“…In the previous work [2], F for a range of small 2 × 10 −6 ≤ x ≤ 1 × 10 −3 and at Q 2 = 590 GeV 2 and then compare with the NNPDF3.0 data [29]. We observe that the LO as well as the NLO effects are much closer to data.…”

“…which is not equal to unity in general as in LO [1,2]. Even if the factor β vanishes, because of the t dependence of the functions…”

“…Which is not equal to unity in general as discussed in LO [1,2] and NLO because of the t dependence of X N N LO 1 (x, t) and X N N LO 2 (x, t) even if β is set to zero. It is to be noted that the term β occuring in eqns.…”

“…Recently we have reported an analysis of the proton structure function as well as the gluon distribution at small x using the Taylor approximated [1,2] DGLAP equations [3][4][5][6]. The precision of the recent experimental data [7] demands the correction terms of the splitting function atleast upto NLO [8,9] and preferrably NNLO [10][11][12] in DGLAP evolution equations.…”