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

Abstract

In this paper we make re-analysis of a self-similarity based model of the proton structure function at small x pursued in recent years. The additional assumption is that it should be singularity free in the entire kinematic range 0 < x < 1. Our analysis indicates that the model is valid in a more restrictive range of Q 2 . We also discuss the possibility of incorporation of Froissart saturation condition in the model.

Froissart Bound and Transverse Momentum Dependent Parton Distribution Functions (TMDPDF) with self-similarity

“…Finally, as noted in earlier publications Ref [42,43] , self-similarity is not a general property of QCD and is not established properly, either theoretically or experimentally. In this work, we have merely made a use of fractal techniques to parametrize a multivarible function like structure function as a method of generalization as in Ref [40].…”

“…We recently suggested self-similar models which are free from such singularity besides having log Q 2 rise in structure function instead of power law rise in Q 2 as reported in Ref [42,43].…”

“…The method of construction of self-similarity based models of Parton Distribution Functions (PDFs) has already been discussed in Ref [41][42][43]. We will outline it for completeness.…”

Froissart bound and self-similarity based models of proton structure functions

“…In this work, we have merely used the notion of self-similarity to parametrize PDFs/structure functions as a generalization of the method suggested in Ref. [44] and reported by us recently in [49,50] and then study how additional conditions among the model parameters are needed to make them compatible with Froissart Bound as well. Besides log 2 (1/x) behavior, the presented models have also power law rise in log Q 2 rather than in Q 2 and are closer to QCD expectation.…”

“…The aim of the present paper is exactly this: we will study the possibility of incorporating Froissart saturation like behaviour in the parametrization of structure function of nucleon based on self-similarity as suggested by Lastovicka [44] and later pursued by us [45][46][47][48][49][50].…”