Speaker
Description
The dimensional renormalization of chiral gauge theories such as the electroweak Standard Model inevitably leads to the problem of accommodating the manifestly 4-dimensional nature of $\gamma_{5}$ in $D$ dimensions. In order to avoid inconsistencies at the multi-loop level, $\gamma_{5}$ can be treated rigorously as a non-anticommuting object using the Breitenlohner-Maison/'t Hooft-Veltman (BMHV) scheme within dimensional regularization (DReg). Employing the BMHV scheme, however, violates gauge invariance, which subsequently needs to be restored using symmetry-restoring counterterms guaranteed to exist by the methods of algebraic renormalization. These counterterms may be calculated via special Feynman diagrams with an insertion of the $\widehat{\Delta}$-operator, which reflects the breaking of chiral gauge invariance, using the regularized quantum action principle of DReg. In the case of an abelian chiral gauge theory this is consistently done at the multi-loop level, showing that the counterterm structure in the BMHV scheme may be written in a very compact form, suitable for computer implementations. While results up to the 2-loop level have already been published, the renormalization procedure has now been performed at the 3-loop level. The UV-divergences are extracted utilizing an infrared rearrangement via the so called all massive tadpoles method, where all occurring Feynman diagrams are mapped to fully massive single-scale vacuum bubbles. Ultimately, this renormalization procedure will be needed for high-precision calculations of e.g. electroweak observables.
