arXiv subjects

Matthias Weißwange

Publications and source records attributed to Matthias Weißwange.

9 recordsLinked to original sources

arXiv2026

Dimensional Regularisation with Non-Anticommuting $γ_5$: Status and Application to the Standard Model

A consistent all-order treatment of $γ_5$ in dimensional regularisation (DReg), as provided by the Breitenlohner-Maison/'t Hooft-Veltman (BMHV) scheme, is essential for high-precision electroweak calculations, but comes at the cost of a regularisation-induced violation of gauge and BRST invariance that must be reinstated via symmetry-restoring counterterms. We report on the current status of our research on the BMHV scheme, from its $D$-dimensional realisation and its multi-loop behaviour up to the 4-loop order, to its most recent application: the complete 1-loop renormalisation of the Standard Model (SM), including both divergent and finite symmetry-restoring counterterms. For the latter, we discuss the main intricacies of the BMHV treatment and present a representative excerpt of the resulting counterterms.

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arXiv2026

Renormalisation of Chiral Gauge Theories with Non-Anticommuting $γ_5$ at the Multi-Loop Level

This thesis presents a comprehensive study of the renormalisation of chiral gauge theories in dimensional regularisation (DReg) at the multi-loop level. We employ the mathematically consistent Breitenlohner-Maison/`t~Hooft-Veltman (BMHV) scheme with non-anticommuting $γ_5$, whose modified algebraic relations induce a spurious violation of gauge and BRST invariance. A central focus is the systematic restoration of the broken symmetry, for which we provide a transparent and fully algorithmic procedure based on the quantum action principle. A major achievement of this work is the complete 4-loop renormalisation of an Abelian chiral gauge theory -- the highest-order application of the BMHV scheme to date. This calculation is made possible by an automated, high-performance computational framework incorporating several optimised algorithms. Our results demonstrate that a rigorous, self-consistent treatment of $γ_5$ is feasible even at very high loop orders. We further analyse dimensional ambiguities and evanescent details corresponding to different implementations of the regularisation, and identify practically efficient prescriptions for $D$-dimensional fermions and gauge interactions. Building on these insights, we present the complete 1-loop renormalisation of the full Standard Model (SM) in the BMHV scheme, providing a first step towards a fully self-consistent multi-loop renormalisation of the SM and establishing a solid foundation for future high-precision electroweak phenomenology.

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arXiv2025

Four-Loop Renormalisation of Chiral Gauge Theories with Non-Anticommuting $γ_5$ in the BMHV Scheme

We present the complete 4-loop renormalisation of an Abelian chiral gauge theory in the Breitenlohner-Maison / `t Hooft-Veltman (BMHV) scheme. Employing a non-anticommuting $γ_5$ in dimensional regularisation, we determine the full set of symmetry restoring counterterms from the quantum action principle. Our calculation represents the highest-order application of the BMHV framework so far, pushing the limits of a self-consistent treatment of $γ_5$ at the multi-loop level. We describe the computational setup that we developed to perform the computations and discuss key implementation aspects, such as the BMHV algebra and tensor reduction. Our work demonstrates the feasibility of applying the BMHV scheme at high loop orders and establishes a solid foundation for future studies of high-precision electroweak physics.

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arXiv2024

Shedding Light on Evanescent Shadows -- Exploration of non-anticommuting $γ_5$ in Dimensional Regularisation

The mathematical consistency of the BMHV scheme of dimensional regularisation (DReg) comes at the cost of requiring symmetry-restoring counterterms to cancel the regularisation-induced breaking of gauge and BRST invariance. There is no unique way to extend a 4-dimensional theory to $D$ dimensions, and different choices can be made for the dimensionally regularised fermions, evanescent parts of their kinetic terms and evanescent gauge interactions. Here we present a detailed study of the impact of changing such evanescent details. We leverage this freedom to identify a particularly convenient formulation that simplifies practical calculations. In order to thoroughly study the available options, we focus on a general abelian chiral gauge theory including scalar fields and adopt a general approach to the BMHV implementation. This allows for specialisation to various models and different approaches, including those from the literature. Importantly, our model can be specialised to the abelian sector of the Standard Model (SM). Consequently, this article also serves as a roadmap for upcoming applications to the full SM.

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arXiv2024

Advances at the $γ_5$-Frontier

These proceedings discuss the current progress of the no-compromise approach to the dimensional renormalization of chiral gauge theories in the context of the BMHV scheme with non-anticommuting $γ_5$. Despite spuriously breaking BRST-invariance in intermediate steps, it is the only scheme which handles the well-known $γ_5$-problem mathematically consistently. We begin with a brief motivation, followed by an exposition of our methodology. Specifically, we illustrate the symmetry restoration procedure to obtain the required symmetry-restoring counterterms and provide insights into our computational setups, including recent developments. Building up on this, we present recent results and advances for the multi-loop renormalization of Abelian and non-Abelian chiral gauge theories, before concluding this article with a discussion on prospective implementations of the BMHV regularization in SM-like models.

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arXiv2024

Computing Tools for Effective Field Theories

In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning automated tools in this field, the SMEFT-Tools 2022 workshop was held at the University of Zurich from 14th-16th September 2022. The current document collects and summarizes the content of this workshop.

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arXiv2023

Full three-loop Renormalisation of an abelian chiral Gauge Theory with non-anticommuting $γ_5$ in the BMHV Scheme

In this work we present a complete three-loop renormalisation of an abelian chiral gauge theory within the Breitenlohner-Maison/'t Hooft-Veltman (BMHV) scheme of dimensional regularisation (DReg). In this scheme the $γ_5$-matrix appearing in gauge interactions is a non-anticommuting object, leading to a breaking of gauge and BRST invariance. Employing an efficient method based on the quantum action principle, we obtain the complete three-loop counterterm action which serves both to render the theory finite and to restore gauge and BRST invariance. The UV singular counterterms involve not only higher order $ε$-poles but also new counterterm structures emerging at the three-loop level for the first time; the finite symmetry-restoring counterterms are restricted to the same structures as at lower loop orders, just with different coefficients, aligning with our expectations. Both the singular and the finite counterterms include structures which cannot be obtained by the standard multiplicative renormalisation. Our results demonstrate that a rigorous treatment of chiral gauge theories with $γ_5$ defined in the BMHV scheme at the multi-loop level is possible and that the obtained counterterm action is suitable for computer implementations, allowing automated calculations without ambiguities caused by $γ_5$.

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arXiv2023

Introduction to Renormalization Theory and Chiral Gauge Theories in Dimensional Regularization with Non-Anticommuting $γ_5$

This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for $γ_5$. One goal is to show how chiral gauge theories can be renormalized despite the spurious breaking of gauge invariance and how to obtain the required symmetry-restoring counterterms. A second goal is to familiarize the reader with the theoretical basis of the renormalization of chiral gauge theories, the theorems that guarantee the existence of renormalized chiral gauge theories at all orders as consistent quantum theories. Relevant topics include BPHZ renormalization, Slavnov-Taylor identities, the BRST formalism and algebraic renormalization, as well as the theorems guaranteeing that dimensional regularization is a consistent regularization/renormalization scheme. All of these, including their proofs and interconnections, are explained and discussed in detail. Further, these theoretical concepts are illustrated in practical applications with the example of an Abelian and a non-Abelian chiral gauge theory. Not only the renormalization procedure for such chiral gauge theories is explained step by step, but also the results of all counterterms, including the symmetry-restoring ones, necessary for the consistent renormalization are explicitly provided.

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arXiv2023

Quantum scale invariance in gauge theories and applications to muon production

We discuss quantum scale invariance in (scale invariant) gauge theories with both ultraviolet (UV) and infrared (IR) divergences. Firstly, their BRST invariance is checked in two apparently unrelated approaches using a scale invariant regularisation (SIR). These approaches are then shown to be equivalent. Secondly, for the Abelian case we discuss both UV and IR quantum corrections present in such theories. We present the Feynman rules in a form suitable for offshell Green functions calculations, together with their one-loop renormalisation. This information is then used for the muon production cross section at one-loop in a quantum scale invariant theory. Such a theory contains not only new UV poles but also IR poles. While the UV poles bring new quantum corrections (in the form of counterterms), finite or divergent, that we compute, it is shown that the IR poles do not bring new physics. The IR quantum corrections, both finite and divergent, cancel out similarly to the way the IR poles themselves cancel in the traditional approach to IR divergences (in the cross section, after summing over virtual and real corrections). Hence, the evanescent interactions induced by the scale-invariant analytical continuation of the SIR scheme do not affect IR physics, as illustrated at one-loop for the muon production ($e^+ e^- \to μ^+μ^-$) cross section.

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