Decoupling of the structure functions in momentum space based on the Laplace transformation

Abstract

Using Laplace transform techniques, we describe the determination of the longitudinal structure function FL(x,Q2), at the leading-order approximation in momentum space, from the structure function F2(x,Q2) and its derivative with respect to lnQ2 in a kinematical region of low values of the Bjorken variable x. Since the x dependence of F2(x,Q2) and its evolution with Q2 are determined much better by the data than FL(x,Q2), this method provides both a direct check on FL(x,Q2) where measured, and a way of extending FL(x,Q2) into regions of x and Q2 where there are currently no data. In our calculations, we ultilize the Block-Durand-Ha parametrization for the structure function F2(x,Q2) [M. M. Block , .]. We find that the Laplace transform method in momentum space provides correct behaviors of the extracted longitudinal structure function FL(x,Q2) and that our obtained results are in line with data from the H1 Collaboration and other results for FL(x,Q2) obtained using Mellin transform method. Published by the American Physical Society 2024