Functional methods are generalized to two-loop EFT matching and running with manifest gauge covariance, and the hard-region matching formula is proven to all loop orders.
Anomalies From the Covariant Derivative Expansion
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abstract
We revisit the calculation of anomalies for global and gauge symmetries in the framework of the Covariant Derivative Expansion (CDE). Due to the presence of UV divergences, the result is an ambiguous quantity that depends on the regularization procedure and the renormalization scheme. We introduce a class of regulators that facilitate a straightforward evaluation of the anomaly exclusively in $d=4$ spacetime dimensions using the CDE methodology. We derive a master formula for the anomaly that integrates various known results into a unified framework.
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A Guide to Functional Methods Beyond One-Loop Order
Functional methods are generalized to two-loop EFT matching and running with manifest gauge covariance, and the hard-region matching formula is proven to all loop orders.