# Addendum to: A new numerical method for obtaining gluon distribution functions $Gx,Q^2=xgx,Q^2$, from the proton structure function $F 2^{γp}x,Q^2$. - High Energy Physics - Phenomenology

Addendum to: A new numerical method for obtaining gluon distribution functions $Gx,Q^2=xgx,Q^2$, from the proton structure function $F 2^{γp}x,Q^2$. - High Energy Physics - Phenomenology - Download this document for free, or read online. Document in PDF available to download.

Abstract: In a recent Letter entitled -A new numerical method for obtaining gluondistribution functions $Gx,Q^2=xgx,Q^2$, from the proton structure function$F 2^{\gamma p}x,Q^2$- arXiv:0907.4790, we derived an accurate and fastalgorithm for numerically inverting Laplace transforms, which we used inobtaining gluon distributions from the proton structure function $F 2^{\gammap}x,Q^2$. We inverted the function $gs$, where $s$ is the variable inLaplace space, to $Gv$, where $v$ is the variable in ordinary space. Sincepublication, we have discovered that the algorithm does not work if$gs ightarrow 0$ less rapidly than $1-s$, as $s ightarrow\infty$. Althoughwe require that $gs ightarrow 0$ as $s ightarrow\infty$, it can approach 0as ${1\over s^\beta}$, with $0<\beta<1$, and still be a proper Laplacetransform. In this note, we derive a new numerical algorithm for just suchcases, and test it for $gs={\sqrt \pi\over \sqrt s}$, the Laplace transformof ${1\over \sqrt v}$.

Author: Martin M. Block

Source: https://arxiv.org/