Naive intuition about scale decoupling breaks down in the presence of fermion masses. Kinematic enhancements can greatly extend the range where one needs to keep a finite mass in calculations to obtain a correct result at even the $\mathcal{O}(1)$ level. Treating a light fermion as massive though, leads to a known but somewhat obscure paradox, a seeming leading-order sensitivity to an arbitrarily small mass. We show how a proper formulation in effective field theory not only resolves the physical conundrum but also answers the very practical question of when fermion masses are required. This has important implications for the development of shower Monte Carlo event generators above the weak scale.

中文翻译：

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用有效场论解决超共线悖论


在费米子质量存在的情况下，关于尺度解耦的天真的直觉就会崩溃。运动学增强可以极大地扩展需要在计算中保持有限质量以获得正确结果的范围，即使是在 $\mathcal{O}(1)$ 等级。然而，将轻费米子视为质量大的，会导致一个已知但有些模糊的悖论，即对任意小质量的表面上的前序敏感性。我们展示了有效场论中的正确表述如何不仅解决了物理难题，而且还回答了何时需要费米子质量这一非常实际的问题。这对于弱尺度以上流星蒙特卡罗事件发生器的发展具有重要意义。