Eur. Phys. J. C (2010) 65: 1-7
https://doi.org/10.1140/epjc/s10052-009-1195-8

Letter

A new numerical method for obtaining gluon distribution functions G(x,Q ²)=xg(x,Q ²), from the proton structure function

Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA

^* e-mail: mblock@northwestern.edu

Received: 27 July 2009
Published online: 10 November 2009

Abstract

An exact expression for the leading-order (LO) gluon distribution function G(x,Q ²)=xg(x,Q ²) from the DGLAP evolution equation for the proton structure function for deep inelastic γ ^* p scattering has recently been obtained (Block et al., Phys. Rev. D 79:014031, 2009) for massless quarks, using Laplace transformation techniques. Here, we develop a fast and accurate numerical inverse Laplace transformation algorithm, required to invert the Laplace transforms needed to evaluate G(x,Q ²), and compare it to the exact solution. We obtain accuracies of less than 1 part in 1000 over the entire x and Q ² spectrum. Since no analytic Laplace inversion is possible for next-to-leading order (NLO) and higher orders, this numerical algorithm will enable one to obtain accurate NLO (and NNLO) gluon distributions, using only experimental measurements of .