Three-loop Higgs self-coupling beta-function in the Standard Model with complex Yukawa matrices

Three-loop renormalization group equations for the Higgs self-coupling and Higgs mass parameter are recalculated in the case of complex Yukawa matrices, which encompass general flavour structure of the Standard Model. In addition, the anomalous dimensions both for the quantum Higgs field and its vacuum expectation value are presented in the $\overline{MS}$-scheme. A numerical study of the latter quantities is carried out for a certain set of initial parameters.