## Three-loop SM beta-functions for matrix Yukawa couplings.(English)Zbl 1317.81268

Summary: We present the extension of our previous results for three-loop Yukawa coupling beta-functions to the case of complex Yukawa matrices describing the flavour structure of the SM. The calculation is carried out in the context of unbroken phase of the SM with the help of the MINCER program in a general linear gauge and cross-checked by means of MATAD/BAMBA codes. In addition, ambiguities in Yukawa matrix beta-functions are studied.

### MSC:

 81V22 Unified quantum theories 81T17 Renormalization group methods applied to problems in quantum field theory

### Keywords:

standard model; renormalization group

### Software:

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