Misconceptions About the Physics of the QCD Trace Anomaly from Renormalization in a Reducible Basis

Abstract

The QCD trace anomaly is a well-established textbook result in quantum field theory with several prominent features: (1) it arises from the quantum breaking of scale symmetry at ultraviolet (UV) scales, yet is independent of the particular UV regulator used, whether lattice or dimensional regularization; (2) although it is nominally proportional to (${\cal O}(\alpha_s)$), it is free of renormalization-scheme ambiguity; and (3) it is free of UV divergences and is therefore scale independent. Unfortunately, these important features have been undermined in the recently introduced reducible-basis renormalization, leading to misunderstandings of anomaly-related nucleon physics, including the origins of nucleon mass and internal forces.