We present a new expansion scheme to compute the rate for parton splittings in dense and finite QCD media. In contrast to the standard opacity expansion, our expansion is performed around the harmonic oscillator whose characteristic frequency depends on the typical transverse momentum scale generated in the splitting. The first two orders account for the high frequency regime that is dominated by single hard scatterings together with the regime of multiple soft scatterings at low frequency. This provides the tools to go beyond the leading logarithmic approximation and compare to the full numerical solution to the corresponding Schrödinger equation across a wide range of gluon frequencies. We investigate the sensitivity of our results to varying the separation scale that defines the leading order. Finally, the application to Monte Carlo event generators is discussed.

中文翻译：

---

改进了介质诱导部分分裂的不透明度扩展

我们提出了一种新的扩展方案来计算密集和有限 QCD 介质中的部分分裂率。与标准不透明度扩展相反，我们的扩展是围绕谐振子进行的，谐振子的特征频率取决于分裂中产生的典型横向动量尺度。前两个阶解释了由单个硬散射和低频多个软散射主导的高频区域。这提供了超越主要对数近似值的工具，并在广泛的胶子频率范围内与相应薛定谔方程的完整数值解进行比较。我们研究了我们的结果对改变定义领先顺序的分离尺度的敏感性。最后，