AI 中文总结
本文通过盖根鲍尔多项式PDF形式，结合核效应与拉普拉斯空间DGLAP演化，分析$xF_3$数据以改进价夸克分布提取，提升了核$xF_3$描述的唯象一致性。
AI 中文摘要
我们对非单态结构函数$xF_3$进行了次领头阶（NLO）和次次领头阶（NNLO）量子色动力学（QCD）分析，采用盖根鲍尔（Gegenbauer）多项式表示来描述输入部分子分布函数（PDFs）。主要目标是评估这种灵活参数化在核效应存在时如何改进价夸克分布的提取。为此，我们将核修正因子纳入重核靶的输入PDFs中，并在拉普拉斯空间中解析求解DGLAP演化方程。随后使用雅可比多项式展开重构Bjorken-$x$空间中的结构函数。该组合框架可系统研究来自CCFR、NuTeV和CHORUS实验的$xF_3$数据，覆盖NLO和NNLO两种精度。我们还检验了提取的分布对核修正的敏感性，并讨论其对格罗斯-卢埃林-史密斯（Gross--Llewellyn Smith）、比约肯（Bjorken）和阿德勒（Adler）求和规则的影响。结果表明，盖根鲍尔多项式PDF形式提供了灵活高效的框架，可描述核$xF_3$数据，在宽运动学范围内产生更好的唯象一致性。
英文摘要
We present a next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) QCD analysis of the non-singlet structure function $xF_3$, utilizing a Gegenbauer-polynomial representation for the input parton distribution functions (PDFs). The main objective is to assess how this flexible parameterization improves the extraction of valence quark distributions in the presence of nuclear effects. To this end, we incorporate nuclear modification factors into the input PDFs for heavy nuclear targets and solve the DGLAP evolution equations analytically in Laplace space. The structure function in Bjorken-$x$ space is then reconstructed using a Jacobi polynomial expansion. This combined framework enables a systematic investigation of the $xF_3$ data from the CCFR, NuTeV, and CHORUS experiments at both NLO and NNLO accuracies. We further examine the sensitivity of the extracted distributions to nuclear corrections and discuss their implications for the Gross--Llewellyn Smith, Bjorken, and Adler sum rules. Our results demonstrate that the Gegenbauer-polynomial PDF formalism provides a flexible and efficient framework for describing nuclear $xF_3$ data, yielding improved phenomenological consistency across a wide kinematic range.
Comments16 pages, 4 figures, 2 tables
