Explicit derivation of the QED trace anomaly in symmetry-preserving loop regularization at one-loop level

Abstract

The QED trace anomaly is calculated at one-loop level based on the loop regularization method which is realized in 4-dimensional space-time and preserves gauge symmetry and Poincar\'e symmetry in spite of the introduction of two mass scales, namely, the ultraviolet (UV) cutoff ${M}_{c}$ and infrared (IR) cutoff ${\ensuremath{\mu}}_{s}$. It is shown that the dilation Ward identity which relates the three-point diagrams with the vacuum polarization diagrams gets the standard form of trace anomaly through quantum corrections in taking the consistent limit ${M}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}$ and ${\ensuremath{\mu}}_{s}=0$ which recovers the original integrals. This explicitly demonstrates that the loop regularization method is indeed a self-consistent regularization scheme which is applicable to the calculations not only for the chiral anomaly but also for the trace anomaly, at least at one-loop level. It is also seen that the consistency conditions which relate the tensor-type and scalar-type irreducible loop integrals (ILIs) are crucial for obtaining a consistent result. As a comparison, we also present the one-loop calculations by using the usual Pauli-Villars regularization and the dimensional regularization.