Longitudinal Structure Function and Parton Distributions in the Light of Self-similarity

Study of parton distributions using the notion of self-similarity was first proposed roughly two decades before. The notion of self-similarity has been well explored to explain the internal structure of proton and gives a new insight to understand parton distributions. In this chapter, longitudinal structure function FL(x, Q2) is evaluated within this approach phenomenologically. Quantum Chromodynamics (QCD) based approximate relations between the longitudinal structure function and the parton distributions have been used in our present study. It is found that the Altarelli-Martinelli equation for the longitudinal structure function cannot be used in Model I because of the presence of a singularity in the Bjorken x-space. The quantitative as well as qualitative analyses of this relation in Model I is thus limited. Cooper-Sarkar et al relation, on the other hand, has been successfully used in both Model I and Model II to evaluate FL(x, Q2). The qualitative characteristic of the prediction of Model II has been observed to be in good agreement with the QCD expectation.