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Analytic inclusion of the scale dependence of the anomalous dimension matrix in Standard Model Effective Theory

  • Andrzej J. Buras
  • Martin Jung
Open Access
Regular Article - Theoretical Physics

Abstract

The renormalization group equations (RGEs) in Standard Model effective theory are usually either solved analytically, neglecting the scale dependence of gauge and Yukawa couplings, or numerically without such approximations. We present analytic solutions of RGEs that take into account the dominant scale dependence of the anomalous-dimension matrix due to the running of the QCD coupling α s and of the top-Yukawa coupling. We consider first the case for which a given operator is generated directly through mixing with the parent operator whose Wilson coefficient is non-vanishing at the new physics scale. Subsequently we consider the case of two-step running, in which two operators do not mix directly, but only via a third mediator operator. We generalize these solutions to an arbitrary number of operators and show how even in this case analytic solutions can be obtained.

Keywords

Beyond Standard Model Effective Field Theories Renormalization Group Resummation 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.TUM Institute for Advanced StudyGarchingGermany
  2. 2.Physik Department, Technische Universität MünchenGarchingGermany
  3. 3.Excellence Cluster Universe, Technische Universität MünchenGarchingGermany

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