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We study the application of the Breitenlohner-Maison-'t Hooft-Veltman (BMHV)scheme of Dimensional Regularization to the renormalization of chiral gaugetheories, focusing on the specific counterterm structure required by thenon-anticommuting Dirac $\gamma_5$ matrix and the breaking of the BRSTinvariance. Calculations are performed at the one-loop level in a masslesschiral Yang-Mills theory with chiral fermions and real scalar fields. Wediscuss the setup and properties of the regularized theory in detail. Ourcentral results are the full counterterm structures needed for the correctrenormalization: the singular UV-divergent counterterms, including evanescentcounterterms that have to be kept for consistency of higher-loop calculations.  We find that the required singular, evanescent counterterms associated withvector and scalar fields are uniquely determined but are not gauge invariant.Furthermore, using the framework of algebraic renormalization, we determine thesymmetry-restoring finite counterterms, that are required to restore the BRSTinvariance, central to the consistency of the theory. These are the necessarybuilding blocks in one-loop and higher-order calculations.  Finally, renormalization group equations are derived within this framework,and the derivation is compared with the more customary calculation in thecontext of symmetry-invariant regularizations. We explain why, at one-looplevel, the extra BMHV-specific counterterms do not change the results for theRGE. The results we find complete those that have been obtained previously inthe literature in the absence of scalar fields.

the journal of high energy physics/the journal of high energy physics

Dimensional Regularization and Breitenlohner-Maison / 't Hooft-Veltman  Scheme for $\gamma_5$ applied to Chiral YM Theories: Full One-Loop  Counterterm and RGE Structure