The Chiral Anomaly in SCET

TL;DR

This paper investigates the manifestation of the chiral anomaly within Soft Collinear Effective Theory (SCET), analyzing its structure up to NNLO and confirming the correspondence with QCD through explicit one-loop calculations.

Contribution

It provides the first detailed computation of the chiral anomaly in SCET up to NNLO, clarifying how anomaly equations are realized at different power expansion orders.

Findings

Anomaly equations in SCET are derived up to NNLO in power counting.

The correspondence between QCD and SCET anomaly equations is validated by one-loop calculations.

The study reveals how anomalies manifest in effective theories with multiple scales.

Abstract

Anomalies are an infrared effect, but are often realized in effective theories in a non-trivial 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 NNLO in the power counting with external collinear and/or ultrasoft gluons. We do this by expanding the QCD anomaly equation, using the tree level (LO in \alpha_s) 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.