Chiral anomaly in soft collinear effective theory

Anomalies have infrared and ultraviolet ingredients, and are often realized in effective theories in a nontrivial way. We study the chiral anomaly in soft collinear effective theory (SCET), where the anomaly equation has terms contributing at different orders in the power expansion. The chiral anomaly equations in SCET are computed up to next-to-next-to-leading order in the power counting with external collinear and/or ultrasoft gluons. We do this by expanding the QCD anomaly equation, using the tree level (leading order in αs) relations between QCD and SCET fields. The validity of this correspondence between the anomaly equations is confirmed by direct computation of the one-loop diagrams in SCET.