The gamma5-problem of dimensional regularization - the HVBM scheme for the electroweak Standard Model at the 2-loop level

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A fundamental fact of nature of the existence of electroweak interactions which violate parity (essentially left-right symmetry). Its technical description uses the so-called gamma5-matrix. Since the seminal work of 't Hooft and Veltman in 1972, dimensional regularization (DREG) provides a mathematically consistent and extremely successful framework for high-precision in elementary particle theory. However, already 't Hooft and Veltman pointed out a problem with gamma5. The problem means in essence that DREG allows no treatment of gamma5 which is simultaneously mathematically consistent and computationally straightforward. Among the many proposals to treat gamma5, there is only one for which rigorous proofs and mathematical consistency have been established: the original one by 't Hooft/Veltman and Breitenlohner/Maison (HVBM scheme). However the HVBM scheme is difficult to apply in practice to the electroweak interactions where gamma5 is ubiquitous and where HVBM breaks an important gauge invariance. Therefore, practioners have traditionally applied alternative schemes which are technically easier to use but have other drawbacks such as limited (sometimes unclear) range of validity and/or lack of mathematical consistency (possibly leading to wrong or ambiguous results). The future need for precise predictions has increased the interest in the gamma5-problem. All recent discussions have focused on alternatives to HVBM and have confirmed the unsatisfactory status and the limitations of alternative schemes, highlighting the need for further work and progress. Hence a complementary, no-compromise study focusing directly on the HVBM scheme seems promising, timely and valuable. Here we propose such a study. We will use the HVBM scheme and apply it to the electroweak Standard Model at the two-loop level, significantly beyond the current status. The goal is to establish how to do HVBM-scheme multi-loop computations in realistic theories and facilitate future two- and three-loop computations of this kind. The research plan consists of a systematic sequence of five steps which are applied at the one-loop and two-loop level first to simpler models and then to the full electroweak Standard Model. A major deliverable is the determination of so-called gauge invariance-restoring and evanescent counterterms --- these are universal building blocks which will be published as computer codes and which will allow to carry out future HVBM computations in a straightforward way. In addition the project will answer several crucial conceptual questions, related to the relationship between HVBM-based and more traditional calculations and related to the pros and cons of various options within the HVBM scheme. In this way the project will also provide important feedback on the traditional schemes, which can be verified and improved by comparing with the rigorous HVBM results.