Resolving the Ultracollinear Paradox with Effective Field Theory

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 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 answers the very practical question of when fermion masses are required. This has important implications for the development of shower Monte Carlo above the weak scale.