论文标题
大型$ n_ \ mathrm {c} $以外的临近领先顺序Balitsky-Kovchegov方程
Next-to-leading order Balitsky-Kovchegov equation beyond large $N_\mathrm{c}$
论文作者
论文摘要
我们计算有限的 - $ n_ \ mathrm {c} $校正临近订单（NLO）balitsky-kovchegov（bk）方程。我们发现使用高斯近似值的两点函数的六个威尔逊线的必要相关器的分析表达式。在合适的基础上，该问题从六六矩阵的对角线化减少到三分三矩阵的对角线化，可以很容易地通过分析进行。我们以数字研究这些有限的$ n_ \ mathrm {c} $校正在NLO BK方程式上。通常，我们发现有限的$ n_ \ mathrm {c} $更正小于预期的$ 1/n_ \ mathrm {c}^2 \ sim 10 \％$。对于单个相关器，校正可能很大，但对振幅的形状影响较小，这是偶极子大小的函数。它们对进化速度的影响甚至较小。
We calculate finite-$N_\mathrm{c}$ corrections to the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation. We find analytical expressions for the necessary correlators of six Wilson lines in terms of the two-point function using the Gaussian approximation. In a suitable basis, the problem reduces from the diagonalization of a six-by-six matrix to the diagonalization of a three-by-three matrix, which can easily be done analytically. We study numerically the effects of these finite-$N_\mathrm{c}$ corrections on the NLO BK equation. In general, we find that the finite-$N_\mathrm{c}$ corrections are smaller than the expected $1/N_\mathrm{c}^2 \sim 10\%$. The corrections may be large for individual correlators, but have less of an influence on the shape of the amplitude as a function of the dipole size. They have an even smaller effect on the evolution speed as a function of rapidity.
