The gamma5-problem of dimensional regularization - the BMHV scheme for the electroweak Standard Model and effective field theories at the 2-loop level and beyond

• Applicant: Professor Dr. Dominik Stöckinger
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 442084807

A fundamental property of nature is the violation of parity (essentially left-right symmetry) by the electroweak interactions. Its technical description uses the so-called gamma5-matrix. Already in their seminal work on dimensional regularization (DREG) and renormalization of gauge theories, 't Hooft and Veltman pointed out a problem with gamma5. In essence, 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 (BMHV scheme). However the BMHV scheme is difficult to apply in practice to the electroweak interactions where gamma5 is ubiquitous and where BMHV breaks an important gauge invariance. Particle physics of the coming decade will be increasingly dominated by detailed tests of all properties of the Standard Model (SM). This requires more and more accurate and reliable theory predictions, including (multi-)loop corrections in the SM involving electroweak interactions and in effective theories related to the SM. Therefore, the gamma5-problem becomes more and more acute and relevant for important computations. The community is aware of this and interested in systematic progress on the issue, as evidenced by recent publications and workshops. Our research project aims for a no-compromise study focusing directly on the consistent BMHV scheme and establishing its use for multi-loop computations in realistic theories with electroweak interactions. In the first funding period, major conceptual questions were answered, we established how to determine the breaking of gauge invariance and the required symmetry-restoring counterterms and renormalization-group beta functions efficiently. The method was validated in multiple ways and applied in generic gauge theories at the 1-loop, 2-loop and even at the 3-loop level. The approach and the results have been extensively interpreted and compared with other formalisms. The technical feasibility of our computations has been demonstrated up to the 3-loop level and preliminary studies and planned collaborations are in place to enable applications to the SM and to effective field theories. In the second funding period we will go to higher loop levels, where the advantages of the BMHV scheme become more significant, we will apply the method to the full SM including electroweak interactions such that BMHV multi-loop computations in realistic theories become possible, and we will treat phenomenologically important effective field theories which are used to parametrized new physics effects and to approximate the SM systematically.

• DFG Programme: Research Grants