Improving the understanding and the applicability of regularization by dimensional reduction for ultraviolet and infrared divergences

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Regularization is a fundamental step in the renormalization of quantum field theories. It replaces divergent integrals by well-defined expressions and thus allows a mathematically consistent definition of quantum field theories. For practical purposes it is desirable that a regularization scheme preserves as many fundamental properties (such as Lorentz invariance or other symmetries) as possible, but no ideal scheme exists. We consider regularization by dimensional reduction (DRED). Particularly for supersymmetric theories DRED is often the best choice. However, several problems of DRED have been known for decades. In spite of recent progress, these problems have again been highlighted by the report of the SPA (“Supersymmetry Parameter Analysis”) collaboration, a world-wide collaboration with more than 100 authors. Our research project is precisely focused on the two most pressing problems of DRED: consistency with supersymmetry and consistency with factorization of infrared divergences. We will give definite answers by proving supersymmetry of DRED in several cases, identifying and describing cases where DRED violates supersymmetry, and by proving consistency with factorization at the two-loop level. Furthermore, we will provide easy-to-use transition rules between DRED and dimensional regularization (DREG). In this way we will significantly improve the theoretical understanding and the practical applicability of DRED and complete one of the seven tasks put forward by the SPA report.