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 O(λ²) are given in terms of these new fields. We then give a simple procedure for constructing power suppressed soft-collinear operators in SCETII by using an intermediate theory SCETI.
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Bauer et al. (2003) studied this question.
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