The Longitudinal Structure Function FL as a Function of F2 and dF2/dln Q2 at Small x. The Next-to-Leading Analysis

We present a set of formulas to extract the longitudinal deep inelastic structure function FL from the transverse structure function F2 and its derivative dF2/dlnQ2 at small x. Our expressions are valid for any non-negative value of δ, with x-δ the behavior of the parton densities at low x. Using F2 HERA data we obtain FL in the range 10-4≤ x≤10-2 at Q2=20 GeV2. Some other applications of the formulas are pointed out.