Decoupling of the DGLAP evolution equations by Laplace method

Abstract

In this paper, we derive two second- order of differential equation for the gluon and singlet distribution functions by using the Laplace transform method. We decoupled the solutions of the singlet and gluon distributions into the initial conditions (function and derivative of the function) at the virtuality $Q_0^2$ separately as these solutions are defined by: \begin{eqnarray} F_{2}^{s}(x,Q^{2}) &=& \mathcal{F}(F_{s0}, \partial F_{s0})\nonumber &&\mathrm{and} \nonumber G(x,Q^{2}) &=& \mathcal{G}(G_{0}, \partial G_{0}).\nonumber \end{eqnarray} We compared our results with the MSTW parameterization and the experimental measurements of $F_2^p(x,Q^2)$.

10 pages, 3 figures

References in corpus (3)

• Parton distributions for the LHC
• Analytic Expression for the Joint x and Q^2 Dependences of the Structure Functions of Deep Inelastic Scattering
• Small x Behavior of Parton Distributions from the Observed Froissart Energy Dependence of the Deep Inelastic Scattering Cross Section

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