The leading three-loop corrections to the Fermi decay constant in the pure MS scheme are computed, shifting the Standard Model Higgs VEV down by about 3.5 MeV and cutting residual scale dependence to below 2e-6.
Top-Yukawa effects on the $\beta$-function of the strong coupling in the SM at four-loop level
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abstract
We present analytical results for the QCD $\beta$-function extended to the gaugeless limit of the unbroken phase of the Standard Model at four-loop level. Apart from the strong coupling itself we include the top-Yukawa contribution and the Higgs self-coupling. We observe a non-naive $\gamma_5$ contribution at order $y_t^4 g_s^4$, a feature not encountered in lower loop orders.
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Three-loop corrections to the Fermi decay constant in the $\overline{\rm{MS}}$ scheme
The leading three-loop corrections to the Fermi decay constant in the pure MS scheme are computed, shifting the Standard Model Higgs VEV down by about 3.5 MeV and cutting residual scale dependence to below 2e-6.