超越程函近似的偶极胶子分布的高能演化
High Energy Evolution of Dipole Gluon Distribution Beyond Eikonal Approximation
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中文总结 AI 辅助
研究超越程函近似的偶极胶子分布高能演化，确定次程函算子，推导其高能演化方程，该方程与威尔逊线偶极关联函数耦合含饱和效应，结果构成首个封闭非线性演化方程，助力小\(x\)唯象学及与中等\(x\)动力学联系。
中文摘要 AI 辅助
在高能情况下，偶极胶子分布由威尔逊线偶极关联函数在程函阶描述，其高能演化由巴利茨基 - 科夫切戈夫方程支配。超越程函近似，我们确定了表示偶极胶子分布的次程函算子，它由带有光锥色电场单次插入的威尔逊线组成，并在单对数近似下，在大\(N_c\)极限中推导其高能演化方程。所得非线性演化与威尔逊线偶极关联函数耦合并包含胶子饱和效应。在稀释极限下，次程函分布随能量以\(\alpha_s N_c/2\pi\)的幂律增长，小于程函值的五分之一，而在饱和区域它遵循与程函关联函数相同的莱文 - 图钦定律。这些结果构成了次程函阶偶极胶子分布的首个封闭非线性演化方程，朝着精确的小\(x\)唯象学以及将小\(x\)物理与中等\(x\)动力学联系起来迈进了一步。
英文摘要
At high energy, the dipole gluon distribution is described at eikonal order by the Wilson-line dipole correlator, whose high-energy evolution is governed by the Balitsky-Kovchegov equation. Going beyond the eikonal approximation, we identify the subeikonal operator representing the dipole gluon distribution, consisting of a Wilson line with a single insertion of the light-cone chromoelectric field, and derive its high-energy evolution equation in the large-$N_c$ limit under the single-logarithmic approximation. The resulting nonlinear evolution is coupled to the Wilson-line dipole correlator and incorporates gluon saturation effects. In the dilute limit, the subeikonal distribution grows as a power-law of the energy with exponent $α_s N_c/2π$, less than one fifth of the eikonal value, while in the saturation regime it obeys the same Levin--Tuchin law as the eikonal correlator. These results constitute the first closed nonlinear evolution equation for the dipole gluon distribution at subeikonal order, a step toward precision small-$x$ phenomenology and toward connecting small-$x$ physics with the moderate-$x$ dynamics.
