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

Self-similarity based model of proton structure function at small x was reported in the literature sometime back. The phenomenological validity of the model is in the kinematical region 6.2×10^-7 ≤x ≤ 10^-2 and 0.045 ≤ Q² ≤120 GeV². 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 (x,Q²) for Altarelli-Martinelli equation in QCD and is compared with the recent HERA data.