Longitudinal structure function FL of proton from Regge-like behaviour of gluon distribution function up to next-to-next-to-leading order at small-x

Abstract

The behaviour of the longitudinal structure function FL with respect to the Bjorken variable x and Q2, the squared four-momentum transfer between lepton and nucleon, in the next-to-next-to-leading order (NNLO) at small x is presented using the Regge-like behaviour of the gluon distribution function. Here we have calculated \( t \left(=\ln \frac{Q^{2}}{\Lambda^{2}}\right)\) - and x -evolutions of the FL structure function using the gluon distribution function obtained as a result of solution of the DGLAP evolution equation at small x . We have also studied the behaviour of the DIS cross section ratio R in this kinematical region. The calculated results are compared with recent H1, ZEUS data and DL model results, CT10 parameterization. The results obtained can be explained within the framework of perturbative quantum chromodynamics i.e., the evolution of the structure function FL increases towards low values of x .