Momentum Fractions of Quarks and Gluons in a Self-Similarity Based Model of Proton

Abstract

In this paper, we use momentum sum rule to compute the fractions of momentum carried by quarks and gluons in a self-similarity based model of proton. Comparison of the results with the prediction of QCD asymptotics is also made.

Momentum fractions carried by quarks and gluons in models of proton structure functions at small x

“…From Table III, we observe that as in Ref [22], in the improved analysis too, x q increases with the increasing Q 2 . On the other hand, column Results of x q of Model 1 for semi-analytical, numerical method and upper limit of x g for numerical method for different Q 2 also decreases with the corresponding increasing Q 2 as in [21].…”

“…However, the phenomenological analysis has one inherent limitation: Due to the negative value of D 3 , Eqn(6) develops a singularity at x 0 ∽ 0.019 [21,22], as it satisfies the condition 1…”

“…One limitation of Ref [21,22] was that the analytical expression for x q contains two infinite series ; one in z ∼ log 1 x and the other in µ 1 ∼ log Q 2 , but only the leading term of each series was considered without studying their convergence properties. This might make the result unstable and unreliable.…”

A Lower Bound on Longitudinal Structure Function at Small x from a Self-Similarity Based Model of Proton

“…Its value has been determined from data in our earlier paper [9] and is found to be approximately equal to 3.1418 (for fractional charged quarks). For integral charged partons, a = 1 [10].…”

An Improved Singularity Free Self-Similar Model of Proton Structure Function

“…Self-similarity is a possible feature of multi-partons inside a proton at small x suggested by Lastovicka [1] and pursued by us in recent years [2,3,4,5,6]. More recently, we have examined its consequences in [7] double parton distribution function(dPDF) to be tested at LHC, in Froissart saturation [8] and Longitudinal structure function [9].…”