The Longitudinal Structure Function F${}_L$ as a Function of F${}_2$ and dF${}_2$/dlnQ${}^2$ at small x. The Next-to-Leading Analysis

Abstract

We present a set of formulae to extract the longitudinal deep inelastic structure function $F_L$ from the transverse structure function $F_2$ and its derivative $d{F}_2/dln{Q}^2$ at small $x$. Our expressions are valid for any value of $\hat{I}´$, being $x^{-\hat{I}´}$ the behavior of the parton densities at low $x$. Using $F_2$ HERA data we obtain $F_L$ in the range $10^{-4}\le x\le 10^{-2}$ at $Q^2=20$ GeV${}^2$. Some other applications of the formulae are pointed out.

Latex file, 10 pages, 2 postscript figures