## 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.

Original language | English |
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Article number | 67 |

Journal | Journal of High Energy Physics |

Volume | 2018 |

Issue number | 6 |

DOIs | |

State | Published - 2018 |

## Keywords

- Beyond standard model
- Effective field theories
- Renormalization group
- Resummation