On-shell amplitude methods allow to derive one-loop renormalization effects from just tree-level amplitudes, with no need of loop calculations. We derive a simple formula to obtain the anomalous dimensions of higher-dimensional operators from a product of tree-level amplitudes. We show how this works for dimension-6 operators of the Standard Model, providing explicit examples of the simplicity, elegance and efficiency of the method. Many anomalous dimensions can be calculated from the same Standard Model tree-level amplitude, displaying the attractive recycling aspect of the on-shell method. With this method, it is possible to relate anomalous dimensions that in the Feynman approach arise from very different diagrams, and obtain non-trivial checks of their relative coefficients. We compare our results to those in the literature, where ordinary methods have been applied.

壳上振幅方法允许仅从树级振幅得出一回路重归一化效果，而无需回路计算。我们导出一个简单的公式，以从树级幅度的乘积中获得高维算子的异常维。我们将展示此方法对标准模型的6维运算符的工作原理，并提供该方法的简单，优雅和高效的显式示例。可以从同一标准模型树级别的振幅计算出许多异常尺寸，这显示了机壳方法有吸引力的回收方面。使用这种方法，可以将在费恩曼方法中由非常不同的图产生的异常尺寸关联起来，并获得对其相对系数的简单检验。我们将我们的结果与文献中的结果进行比较，