Power suppressed operators and gauge invariance in soft-collinear effective theory

The form of collinear gauge invariance for power suppressed operators in the soft-collinear effective theory (SCET) is discussed. Using a field redefinition we show that it is possible to make any power suppressed ultrasoft-collinear operators invariant under the original leading order gauge transformations. Our manipulations avoid gauge fixing. The Lagrangians to script O sign(λ²) are given in terms of these new fields. We then give a simple procedure for constructing power suppressed soft-collinear operators in SCET_II by using an intermediate theory SCET_I.