Improved Method to extract Nucleon Helicity Distributions using Event Weighting

TL;DR

This paper presents an improved method for extracting nucleon helicity distributions from deep inelastic scattering data by using event weighting based on the energy fraction of produced hadrons, enhancing statistical precision.

Contribution

The novel aspect is the application of a weighting procedure that leverages the energy dependence of fragmentation functions to improve the extraction of quark helicity distributions in LO QCD.

Findings

Achieved 15-39% improvement in figure of merit depending on quark flavor and z cut.

Demonstrated the method's effectiveness through numerical examples.

Provided a mathematical framework for optimal parameter estimation in this context.

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 $\boldsymbol \Theta$ determined from a system of linear equations ${\bf B}(x) {\boldsymbol \Theta} ={\bf Y}(x)$, where the measured input vector ${\bf Y}(x)$ is given as event distributions depending on a random variable $x$, the coefficients of the matrix ${\bf B}(x)$ depend as well on $x$, whereas the parameter vector $\boldsymbol\Theta$ to be determined does not.