一种改进的基于事例加权的核子螺旋度分布提取方法
Improved Method to extract Nucleon Helicity Distributions using Event Weighting
摘要：
提出了一种改进的从深度非弹性散射中的半包含双自旋不对称性提取首阶QCD中夸克螺旋度分布的分析方法。该方法依赖于这样一个事实，即碎裂函数，描述的夸克碎裂成强子，有很强的依赖于所观察到的强子的能量分数$z$。具有大$z$的强子包含更多关于撞击夸克的信息。这可以在加权过程中使用，以提高品质因数（=方差的倒数）。在数值例子中表明，根据夸克味和对$z$的削减，可以获得15- 39%的增益.在数学上，该问题可以被描述为根据从线性方程组${\bf B}(x) {\boldsymbol Θ} ={\bf Y}(x)$确定的参数$\boldsymbol Θ$的品质因数找到最优解，其中测量的输入矢量${\bf Y}(x)$被给出为取决于随机变量$x$的事件分布，矩阵${\bf B}(x)$的系数也取决于$x$，而待确定的参数矢量$\boldsymbolΘ$不取决于$x$。
英文摘要：
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 $\boldsymbol Θ$ determined from a system of linear equations ${\bf B}(x) {\boldsymbol Θ} ={\bf Y}(x)$, 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 $\boldsymbolΘ$ to be determined does not.
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