存在测量δ函数时的分部积分恒等式
Integration-by-parts identities in the presence of measurement delta functions
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中文总结 AI 辅助
本文推导了含测量δ函数的维数正规化圈积分的IBP恒等式便利形式，可用于非线性测量函数的微分分布计算，并在QCD相关过程的横动量分布中完成了验证。
中文摘要 AI 辅助
我们推导了包含由δ分布δ(φ(ℓ))施加的测量约束的维数正规化圈积分的分部积分（IBP）恒等式的便利形式，其中φ是圈动量的正则且通常为非线性函数。可直接由与超曲面φ=0相切的向量生成非平凡的IBP关系，使测量δ作为整体因子，避免了分布的导数。该构造为非线性测量函数（尤其是横动量分布）的反向幺正性内的微分分布提供了系统途径。我们在QCD领头阶的t\bar{t}H产生和次领头阶的t\bar{t}产生的横动量分布中实现该构造并进行验证。
英文摘要
We derive a convenient form of integration-by-parts (IBP) identities for dimensionally regulated loop integrals that include a measurement constraint imposed by a delta distribution $δ(ϕ(\ell))$, where $ϕ$ is a regular and generally non-linear function of the loop momentum. Non-trivial IBP relations can be generated directly by vectors tangent to the hypersurface $ϕ=0$, leaving the measurement delta as an overall factor and avoiding derivatives of distributions. This construction provides a systematic route to differential distributions within reverse unitarity for non-linear measurement functions, in particular, for transverse-momentum distributions. We implement the construction and validate it for transverse-momentum distributions in $t\bar tH$ production at leading order and $t\bar t$ production at next-to-leading order in QCD.
