AI 中文总结
本文在软共线有效理论框架下，推导了阈值区域端点DIS的次领头幂次因子化定理，解决了端点发散，重求和领头对数并建立了两种PDF定义的全阶关系。
AI 中文摘要
我们在领头扭度下，研究阈值区域$x\to1$时超越$1-x$领头幂次的深度非弹性散射（DIS）。在坐标空间软共线有效理论框架下，我们推导了非对角部分子散射道的因子化定理，该定理始于次领头幂次（NLP）。强子张量可分离为来自幂次压低流的反硬共线贡献，以及来自亚领头拉格朗日相互作用的软共线贡献，其卷积积分呈现端点发散。我们证明这些发散可通过端点因子化关系解决，这意味着阈值附近的部分子分布函数（PDF）在NLP下成为双尺度对象。我们推导了大$x$下次领头幂次胶子分布的因子化，该因子化涉及硬共线匹配系数与扣除后的软共线函数。我们对$1-x$的领头对数进行了重求和，既包括在$\overline{\text{MS}}$方案下的$d$维因子化，也包括基于再因子化的端点方案，并建立了两种PDF定义之间的全阶关系。
英文摘要
We study deep-inelastic scattering (DIS) in the threshold region $x\to 1$ beyond leading power in $1-x$ at leading twist. In the framework of position-space soft-collinear effective theory, we derive a factorization theorem for the off-diagonal parton-scattering channel, which starts at next-to-leading power (NLP). The hadronic tensor separates into an anti-hardcollinear contribution from power-suppressed currents and a soft-collinear contribution from subleading Lagrangian interactions, whose convolution integrals exhibit endpoint divergences. We show that these divergences are resolved by endpoint factorization relations, implying that the parton distribution function (PDF) near threshold becomes a two-scale object at NLP. We derive the factorization of the NLP gluon distribution at large $x$ in terms of hardcollinear matching coefficients and a subtracted soft-collinear function. We resum the leading logarithms of $1-x$ both from $d$-dimensional factorization in the $\overline{\rm MS}$ scheme and in an endpoint scheme based on refactorization, and establish the all-order relation between the two definitions of the PDF.
Comments59 pages
