Evolution of the longitudinal structure function at small x

Abstract

We derive an approximation approach to evolution of the longitudinal structure function, by using a Laplace-transform method. We solve the master equation and derive the longitudinal structure function as a function of the initial condition $F_L(x,Q_0^2)$ at small x. Our results are independent of the longitudinal coefficient functions and extend from the leading order (LO) up to next-to-next-to-leading order (NNLO). The comparisons with H1 data and other parameterizations are made and results show that they are in agreement with H1 data and some phenomenological models.

Comments: 8pages,3figures