A lower bound on the Longitudinal Structure Function at small x from a self-similarity based model of Proton

Abstract

Self-similarity based model of proton structure function at small \textit{x} was reported in the literature sometime back. The phenomenological validity of the model is in the kinematical region $6.2\times 10^{-7}\le x\le 10^{-2}$ and $0.045\le Q^2\le 120\mathrm{Ge}{\mathrm{V}}^2$. We use momentum sum rule to pin down the corresponding self-similarity based gluon distribution function valid in the same kinematical region. The model is then used to compute bound on the longitudinal structure function $F_L\left(x,Q^2\right)$ for Altarelli-Martinelli equation in QCD and is compared with the recent HERA data.

Comments: 10 pages, 3 figures. arXiv admin note: text overlap with arXiv:1004.1440 by other authors