Improved Method to extract Nucleon Helicity Distributions using Event Weighting

Abstract

An improved analysis method to extract quark helicity distributions in leading order (LO) QCD from semi-inclusive double spin asymmetries in deep inelastic scattering is presented. The method relies on the fact that fragmentation functions, describing the fragmentation of a quark into a hadron, have a strong dependence on the energy fraction $z$ of the observed hadron. Hadrons with large $z$ contain more information about the struck quark. This can be used in a weighting procedure to improve the figure of merit (= inverse of variance). In numerical examples it is shown that one could gain 15-39\% depending on the quark flavor and cut on $z$. Mathematically the problem can be described as finding an optimal solution in terms of the figure of merit for parameters $\mathbf{\Theta }$ determined from a system of linear equations $\mathbf{B}(x)\mathbf{\Theta }=\mathbf{Y}(x)$, where the measured input vector $\mathbf{Y}(x)$ is given as event distributions depending on a random variable $x$, the coefficients of the matrix $\mathbf{B}(x)$ depend as well on $x$, whereas the parameter vector $\mathbf{\Theta }$ to be determined does not.

Comments: 13 pages, 3 figures