Gluon distribution and $dF_2/d$ ln $Q^2$ at small $x$ in the next-to-leading order

Abstract

We obtain an approximate form of gluon momentum density \(G(x, Q^2)\) from next to leading order (NLO) GLAP equation at low \(x\), with a factorization ansatz recently reported and test its validity by comparing it with that of Gluck, Reya and Vogt (GRV-HO) which has no such additional assumption. Using Prytz's approximate method, we calculate \(dF_2/d\log Q^2\) using LO and NLO forms of gluon density. Limitation of the present formalism is critically discussed and approximate factorizability zone in (\(x-Q^2\)) plane is indicated.