Effective field theory approach to soft theorems

I outline an effective theory approach to the expansion of a gauge theory scattering amplitude in the limit that a participating gluon goes soft. The leading order term in the expansion has a well known universal characterization as simple multiplicative eikonal factor of a lower point scattering amplitude. At subleading orders in the soft expansion, one can find an extended version of the universality at tree level in the loop expansion, known as the Low-Burnett-Kroll theorem, where the multiplicative factor acts as a differential operator on the lower point amplitude. However, at loop level, collinear physics spoils this universality at subleading orders, due to a correlated soft and collinear limit of loop integration. Still, using the tools of effective theory, much of the universality found at leading order can be extended to subleading orders, and a complete characterization of new terms in the factorization can be had. The guiding principles will be the reparametrization invariance of the effective theory, and its construction out of manifestly gauge invariant objects.