Partons at small x

Abstract

We give a brief summary of the work on partons at small Bjorken x pursued by us at Gauhati University in recent years. We use both conventional DGLAP method and not so conventional self-similarity inspired method. In DGLAP approach, we solve the QCD evolution equations approximately at small x by two methods- Lagrange's and method of characteristics. We apply them to both spin dependent and spin independent structure functions. In the second approach, we use the notion of self-similarity of fractal geometry to construct Transverse Momentum Dependent Parton Distributions (TMD's), integrated Parton Densities (PDF's) and determine them from HERA collider data. We then use them to compute fractions of momentum carried by quarks and gluons inside the proton and compare with QCD expectations. In view of topical importance of multi parton interactions at LHC at TeV scale, we also outline the construction of Double Parton Distributions (dPDF's) with self-similarity at small x1, x2.